htmldoc regenerated

1 files changed, 417 insertions, 181 deletions

diff --git a/docs/htmldoc/mathcomp.algebra.interval.html b/docs/htmldoc/mathcomp.algebra.interval.html
index d10a18d..e0e16ed 100644
--- a/docs/htmldoc/mathcomp.algebra.interval.html
+++ b/docs/htmldoc/mathcomp.algebra.interval.html
@@ -21,7 +21,6 @@
 <div class="code">
 <span class="comment">(*&nbsp;(c)&nbsp;Copyright&nbsp;2006-2016&nbsp;Microsoft&nbsp;Corporation&nbsp;and&nbsp;Inria.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<br/>
 &nbsp;Distributed&nbsp;under&nbsp;the&nbsp;terms&nbsp;of&nbsp;CeCILL-B.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*)</span><br/>
-<span class="id" title="keyword">Require</span> <span class="id" title="keyword">Import</span> <a class="idref" href="mathcomp.ssreflect.ssreflect.html#"><span class="id" title="library">mathcomp.ssreflect.ssreflect</span></a>.<br/>
 
 <br/>
 </div>
@@ -76,31 +75,228 @@
 <br/>
 
 <br/>
-<span class="id" title="keyword">Section</span> <a name="IntervalPo"><span class="id" title="section">IntervalPo</span></a>.<br/>
+<span class="id" title="keyword">Section</span> <a name="LersifPo"><span class="id" title="section">LersifPo</span></a>.<br/>
 
 <br/>
-<span class="id" title="keyword">CoInductive</span> <a name="itv_bound"><span class="id" title="inductive">itv_bound</span></a> (<span class="id" title="var">T</span> : <span class="id" title="keyword">Type</span>) : <span class="id" title="keyword">Type</span> := <a name="BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <span class="id" title="keyword">of</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#bool"><span class="id" title="inductive">bool</span></a> &amp; <a class="idref" href="mathcomp.algebra.interval.html#T"><span class="id" title="variable">T</span></a> | <a name="BInfty"><span class="id" title="constructor">BInfty</span></a>.<br/>
-<span class="id" title="keyword">Notation</span> <a name="BOpen"><span class="id" title="abbreviation">BOpen</span></a> := (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a>).<br/>
-<span class="id" title="keyword">Notation</span> <a name="BClose"><span class="id" title="abbreviation">BClose</span></a> := (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a>).<br/>
-<span class="id" title="keyword">CoInductive</span> <a name="interval"><span class="id" title="inductive">interval</span></a> (<span class="id" title="var">T</span> : <span class="id" title="keyword">Type</span>) := <a name="Interval"><span class="id" title="constructor">Interval</span></a> <span class="id" title="keyword">of</span> <a class="idref" href="mathcomp.algebra.interval.html#itv_bound"><span class="id" title="inductive">itv_bound</span></a> <a class="idref" href="mathcomp.algebra.interval.html#T"><span class="id" title="variable">T</span></a> &amp; <a class="idref" href="mathcomp.algebra.interval.html#itv_bound"><span class="id" title="inductive">itv_bound</span></a> <a class="idref" href="mathcomp.algebra.interval.html#T"><span class="id" title="variable">T</span></a>.<br/>
+<span class="id" title="keyword">Variable</span> <a name="LersifPo.R"><span class="id" title="variable">R</span></a> : <a class="idref" href="mathcomp.algebra.ssrnum.html#Num.NumDomain.Exports.numDomainType"><span class="id" title="abbreviation">numDomainType</span></a>.<br/>
 
 <br/>
-<span class="id" title="keyword">Variable</span> (<a name="IntervalPo.R"><span class="id" title="variable">R</span></a> : <a class="idref" href="mathcomp.algebra.ssrnum.html#Num.NumDomain.Exports.numDomainType"><span class="id" title="abbreviation">numDomainType</span></a>).<br/>
+<span class="id" title="keyword">Definition</span> <a name="lersif"><span class="id" title="definition">lersif</span></a> (<span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.algebra.interval.html#LersifPo.R"><span class="id" title="variable">R</span></a>) <span class="id" title="var">b</span> := <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">then</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation">&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">else</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#cb42ec59ad57b25928e1718b4e69e031"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a>.<br/>
 
 <br/>
-<span class="id" title="keyword">Definition</span> <a name="pred_of_itv"><span class="id" title="definition">pred_of_itv</span></a> (<span class="id" title="var">i</span> : <a class="idref" href="mathcomp.algebra.interval.html#interval"><span class="id" title="inductive">interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>) : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a> :=<br/>
-&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#880a9790dece461a678db8aa0c091f63"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#880a9790dece461a678db8aa0c091f63"><span class="id" title="notation">pred</span></a> <span class="id" title="var">x</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#880a9790dece461a678db8aa0c091f63"><span class="id" title="notation">|</span></a> <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <span class="id" title="var">l</span> <span class="id" title="var">u</span> := <a class="idref" href="mathcomp.algebra.interval.html#i"><span class="id" title="variable">i</span></a> <span class="id" title="tactic">in</span><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="id" title="keyword">match</span> <span class="id" title="var">l</span> <span class="id" title="keyword">with</span><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| <span class="id" title="var">BOpen</span> <span class="id" title="var">a</span> ⇒ <span class="id" title="var">a</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#388c172bf8d34ef0bf11898cd56f8d7b"><span class="id" title="notation">&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| <span class="id" title="var">BClose</span> <span class="id" title="var">a</span> ⇒ <span class="id" title="var">a</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#1065783963a393d1eafa2137291f2495"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| <a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="id" title="keyword">end</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&amp;&amp;</span></a><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="id" title="keyword">match</span> <span class="id" title="var">u</span> <span class="id" title="keyword">with</span><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| <span class="id" title="var">BOpen</span> <span class="id" title="var">b</span> ⇒ <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#388c172bf8d34ef0bf11898cd56f8d7b"><span class="id" title="notation">&lt;</span></a> <span class="id" title="var">b</span><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| <span class="id" title="var">BClose</span> <span class="id" title="var">b</span> ⇒ <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#1065783963a393d1eafa2137291f2495"><span class="id" title="notation">≤</span></a> <span class="id" title="var">b</span><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| <a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="id" title="keyword">end</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#880a9790dece461a678db8aa0c091f63"><span class="id" title="notation">]</span></a>.<br/>
-<span class="id" title="keyword">Canonical</span> <span class="id" title="keyword">Structure</span> <span class="id" title="var">itvPredType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#mkPredType"><span class="id" title="definition">mkPredType</span></a> <a class="idref" href="mathcomp.algebra.interval.html#pred_of_itv"><span class="id" title="definition">pred_of_itv</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="subr_lersifr0"><span class="id" title="lemma">subr_lersifr0</span></a> <span class="id" title="var">b</span> (<span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.algebra.interval.html#LersifPo.R"><span class="id" title="variable">R</span></a>) : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#51dc792c356ca1a71a3094b50d6bb2fb"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> 0 <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="subr_lersif0r"><span class="id" title="lemma">subr_lersif0r</span></a> <span class="id" title="var">b</span> (<span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.algebra.interval.html#LersifPo.R"><span class="id" title="variable">R</span></a>) : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a>0 <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#51dc792c356ca1a71a3094b50d6bb2fb"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="subr_lersif0"><span class="id" title="definition">subr_lersif0</span></a> := <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#subr_lersifr0"><span class="id" title="lemma">subr_lersifr0</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.algebra.interval.html#subr_lersif0r"><span class="id" title="lemma">subr_lersif0r</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">)</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_trans"><span class="id" title="lemma">lersif_trans</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <span class="id" title="var">z</span> <span class="id" title="var">b1</span> <span class="id" title="var">b2</span> :<br/>
+&nbsp;&nbsp;<a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">||</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif01"><span class="id" title="lemma">lersif01</span></a> <span class="id" title="var">b</span> : 0 <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> 1 <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_anti"><span class="id" title="lemma">lersif_anti</span></a> <span class="id" title="var">b1</span> <span class="id" title="var">b2</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> :<br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&amp;&amp;</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">||</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">then</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">else</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersifxx"><span class="id" title="lemma">lersifxx</span></a> <span class="id" title="var">x</span> <span class="id" title="var">b</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b3ebd0deddd84fd60e149cb5ef719351"><span class="id" title="notation">~~</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersifNF"><span class="id" title="lemma">lersifNF</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <span class="id" title="var">b</span> : <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b3ebd0deddd84fd60e149cb5ef719351"><span class="id" title="notation">~~</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersifS"><span class="id" title="lemma">lersifS</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <span class="id" title="var">b</span> : <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation">&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersifT"><span class="id" title="lemma">lersifT</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation">&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.  <br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersifF"><span class="id" title="lemma">lersifF</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#cb42ec59ad57b25928e1718b4e69e031"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.  <br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_oppl"><span class="id" title="lemma">lersif_oppl</span></a> <span class="id" title="var">b</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_oppr"><span class="id" title="lemma">lersif_oppr</span></a> <span class="id" title="var">b</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_0oppr"><span class="id" title="lemma">lersif_0oppr</span></a> <span class="id" title="var">b</span> <span class="id" title="var">x</span> : 0 <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> 0 <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_oppr0"><span class="id" title="lemma">lersif_oppr0</span></a> <span class="id" title="var">b</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> 0 <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a>0 <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_opp2"><span class="id" title="lemma">lersif_opp2</span></a> <span class="id" title="var">b</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#04245d0240efdac4719fcf73ee860591"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#04245d0240efdac4719fcf73ee860591"><span class="id" title="notation">mono</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#a8ac36d488c8d5cdcfec5adcde894e5f"><span class="id" title="notation">-%</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#a8ac36d488c8d5cdcfec5adcde894e5f"><span class="id" title="notation">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#04245d0240efdac4719fcf73ee860591"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#04245d0240efdac4719fcf73ee860591"><span class="id" title="notation">/~</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#04245d0240efdac4719fcf73ee860591"><span class="id" title="notation">}</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="lersif_oppE"><span class="id" title="definition">lersif_oppE</span></a> := <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#lersif_0oppr"><span class="id" title="lemma">lersif_0oppr</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.algebra.interval.html#lersif_oppr0"><span class="id" title="lemma">lersif_oppr0</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.algebra.interval.html#lersif_opp2"><span class="id" title="lemma">lersif_opp2</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">)</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_add2l"><span class="id" title="lemma">lersif_add2l</span></a> <span class="id" title="var">b</span> <span class="id" title="var">x</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#02b248fee5f27b186ea3a36733c25088"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#02b248fee5f27b186ea3a36733c25088"><span class="id" title="notation">mono</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#a87d5ea2e207e69e5e474db24f56d4cb"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#a87d5ea2e207e69e5e474db24f56d4cb"><span class="id" title="notation">R</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#a87d5ea2e207e69e5e474db24f56d4cb"><span class="id" title="notation">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#02b248fee5f27b186ea3a36733c25088"><span class="id" title="notation">:</span></a> <span class="id" title="var">y</span> <span class="id" title="var">z</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#02b248fee5f27b186ea3a36733c25088"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#02b248fee5f27b186ea3a36733c25088"><span class="id" title="notation">}</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_add2r"><span class="id" title="lemma">lersif_add2r</span></a> <span class="id" title="var">b</span> <span class="id" title="var">x</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#02b248fee5f27b186ea3a36733c25088"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#02b248fee5f27b186ea3a36733c25088"><span class="id" title="notation">mono</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#a87d5ea2e207e69e5e474db24f56d4cb"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#a87d5ea2e207e69e5e474db24f56d4cb"><span class="id" title="notation">R</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#d89396f990d6b54d736cfe259e498cf4"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#02b248fee5f27b186ea3a36733c25088"><span class="id" title="notation">:</span></a> <span class="id" title="var">y</span> <span class="id" title="var">z</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#02b248fee5f27b186ea3a36733c25088"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#02b248fee5f27b186ea3a36733c25088"><span class="id" title="notation">}</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="lersif_add2"><span class="id" title="definition">lersif_add2</span></a> := <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#lersif_add2l"><span class="id" title="lemma">lersif_add2l</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.algebra.interval.html#lersif_add2r"><span class="id" title="lemma">lersif_add2r</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">)</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_subl_addr"><span class="id" title="lemma">lersif_subl_addr</span></a> <span class="id" title="var">b</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <span class="id" title="var">z</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#51dc792c356ca1a71a3094b50d6bb2fb"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#c7f78cf1f6a5e4f664654f7d671ca752"><span class="id" title="notation">+</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_subr_addr"><span class="id" title="lemma">lersif_subr_addr</span></a> <span class="id" title="var">b</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <span class="id" title="var">z</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#51dc792c356ca1a71a3094b50d6bb2fb"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.algebra.interval.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#c7f78cf1f6a5e4f664654f7d671ca752"><span class="id" title="notation">+</span></a> <a class="idref" href="mathcomp.algebra.interval.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="lersif_sub_addr"><span class="id" title="definition">lersif_sub_addr</span></a> := <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#lersif_subl_addr"><span class="id" title="lemma">lersif_subl_addr</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.algebra.interval.html#lersif_subr_addr"><span class="id" title="lemma">lersif_subr_addr</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">)</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_subl_addl"><span class="id" title="lemma">lersif_subl_addl</span></a> <span class="id" title="var">b</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <span class="id" title="var">z</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#51dc792c356ca1a71a3094b50d6bb2fb"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#c7f78cf1f6a5e4f664654f7d671ca752"><span class="id" title="notation">+</span></a> <a class="idref" href="mathcomp.algebra.interval.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_subr_addl"><span class="id" title="lemma">lersif_subr_addl</span></a> <span class="id" title="var">b</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <span class="id" title="var">z</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#51dc792c356ca1a71a3094b50d6bb2fb"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.algebra.interval.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#c7f78cf1f6a5e4f664654f7d671ca752"><span class="id" title="notation">+</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="lersif_sub_addl"><span class="id" title="definition">lersif_sub_addl</span></a> := <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#lersif_subl_addl"><span class="id" title="lemma">lersif_subl_addl</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.algebra.interval.html#lersif_subr_addl"><span class="id" title="lemma">lersif_subr_addl</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">)</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_andb"><span class="id" title="lemma">lersif_andb</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.algebra.interval.html#lersif"><span class="id" title="definition">lersif</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">:</span></a> <span class="id" title="var">p</span> <span class="id" title="var">q</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.algebra.interval.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">||</span></a> <a class="idref" href="mathcomp.algebra.interval.html#q"><span class="id" title="variable">q</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">&gt;-&gt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&amp;&amp;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#q"><span class="id" title="variable">q</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">}</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_orb"><span class="id" title="lemma">lersif_orb</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.algebra.interval.html#lersif"><span class="id" title="definition">lersif</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">:</span></a> <span class="id" title="var">p</span> <span class="id" title="var">q</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.algebra.interval.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&amp;&amp;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#q"><span class="id" title="variable">q</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">&gt;-&gt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">||</span></a> <a class="idref" href="mathcomp.algebra.interval.html#q"><span class="id" title="variable">q</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">}</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_imply"><span class="id" title="lemma">lersif_imply</span></a> <span class="id" title="var">b1</span> <span class="id" title="var">b2</span> <span class="id" title="var">r1</span> <span class="id" title="var">r2</span> :<br/>
+&nbsp;&nbsp;<a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#a133e82bab56729f895f9b2b31e837cd"><span class="id" title="notation">==&gt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#r1"><span class="id" title="variable">r1</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#r2"><span class="id" title="variable">r2</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#r1"><span class="id" title="variable">r1</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#r2"><span class="id" title="variable">r2</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersifW"><span class="id" title="lemma">lersifW</span></a> <span class="id" title="var">b</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#cb42ec59ad57b25928e1718b4e69e031"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="ltrW_lersif"><span class="id" title="lemma">ltrW_lersif</span></a> <span class="id" title="var">b</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation">&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_pmul2l"><span class="id" title="lemma">lersif_pmul2l</span></a> <span class="id" title="var">b</span> <span class="id" title="var">x</span> : 0 <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation">&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#02b248fee5f27b186ea3a36733c25088"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#02b248fee5f27b186ea3a36733c25088"><span class="id" title="notation">mono</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#3609d85e23333c9e68741ad96b416eec"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#3609d85e23333c9e68741ad96b416eec"><span class="id" title="notation">R</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#3609d85e23333c9e68741ad96b416eec"><span class="id" title="notation">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#02b248fee5f27b186ea3a36733c25088"><span class="id" title="notation">:</span></a> <span class="id" title="var">y</span> <span class="id" title="var">z</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#02b248fee5f27b186ea3a36733c25088"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#02b248fee5f27b186ea3a36733c25088"><span class="id" title="notation">}</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_pmul2r"><span class="id" title="lemma">lersif_pmul2r</span></a> <span class="id" title="var">b</span> <span class="id" title="var">x</span> : 0 <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation">&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#02b248fee5f27b186ea3a36733c25088"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#02b248fee5f27b186ea3a36733c25088"><span class="id" title="notation">mono</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#3609d85e23333c9e68741ad96b416eec"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#3609d85e23333c9e68741ad96b416eec"><span class="id" title="notation">R</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#d89396f990d6b54d736cfe259e498cf4"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#02b248fee5f27b186ea3a36733c25088"><span class="id" title="notation">:</span></a> <span class="id" title="var">y</span> <span class="id" title="var">z</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#02b248fee5f27b186ea3a36733c25088"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#02b248fee5f27b186ea3a36733c25088"><span class="id" title="notation">}</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_nmul2l"><span class="id" title="lemma">lersif_nmul2l</span></a> <span class="id" title="var">b</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation">&lt;</span></a> 0 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#04245d0240efdac4719fcf73ee860591"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#04245d0240efdac4719fcf73ee860591"><span class="id" title="notation">mono</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#3609d85e23333c9e68741ad96b416eec"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#3609d85e23333c9e68741ad96b416eec"><span class="id" title="notation">R</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#3609d85e23333c9e68741ad96b416eec"><span class="id" title="notation">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#04245d0240efdac4719fcf73ee860591"><span class="id" title="notation">:</span></a> <span class="id" title="var">y</span> <span class="id" title="var">z</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#04245d0240efdac4719fcf73ee860591"><span class="id" title="notation">/~</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#04245d0240efdac4719fcf73ee860591"><span class="id" title="notation">}</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_nmul2r"><span class="id" title="lemma">lersif_nmul2r</span></a> <span class="id" title="var">b</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation">&lt;</span></a> 0 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#04245d0240efdac4719fcf73ee860591"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#04245d0240efdac4719fcf73ee860591"><span class="id" title="notation">mono</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#3609d85e23333c9e68741ad96b416eec"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#3609d85e23333c9e68741ad96b416eec"><span class="id" title="notation">R</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#d89396f990d6b54d736cfe259e498cf4"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#04245d0240efdac4719fcf73ee860591"><span class="id" title="notation">:</span></a> <span class="id" title="var">y</span> <span class="id" title="var">z</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#04245d0240efdac4719fcf73ee860591"><span class="id" title="notation">/~</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#04245d0240efdac4719fcf73ee860591"><span class="id" title="notation">}</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="real_lersifN"><span class="id" title="lemma">real_lersifN</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <span class="id" title="var">b</span> : <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c94c2df86ca03f22f8f8b739cd7e1e88"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c94c2df86ca03f22f8f8b739cd7e1e88"><span class="id" title="notation">is</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#Num.real"><span class="id" title="abbreviation">Num.real</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c94c2df86ca03f22f8f8b739cd7e1e88"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c94c2df86ca03f22f8f8b739cd7e1e88"><span class="id" title="notation">is</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#Num.real"><span class="id" title="abbreviation">Num.real</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;<a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b3ebd0deddd84fd60e149cb5ef719351"><span class="id" title="notation">~~</span></a><a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b3ebd0deddd84fd60e149cb5ef719351"><span class="id" title="notation">~~</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b3ebd0deddd84fd60e149cb5ef719351"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b3ebd0deddd84fd60e149cb5ef719351"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="real_lersif_norml"><span class="id" title="lemma">real_lersif_norml</span></a> <span class="id" title="var">b</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> :<br/>
+&nbsp;&nbsp;<a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c94c2df86ca03f22f8f8b739cd7e1e88"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c94c2df86ca03f22f8f8b739cd7e1e88"><span class="id" title="notation">is</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#Num.real"><span class="id" title="abbreviation">Num.real</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ssrnum.html#55297ec87c6b3f98c14c99daeafb55d3"><span class="id" title="notation">`|</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.algebra.ssrnum.html#55297ec87c6b3f98c14c99daeafb55d3"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&amp;&amp;</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="real_lersif_normr"><span class="id" title="lemma">real_lersif_normr</span></a> <span class="id" title="var">b</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> :<br/>
+&nbsp;&nbsp;<a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c94c2df86ca03f22f8f8b739cd7e1e88"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c94c2df86ca03f22f8f8b739cd7e1e88"><span class="id" title="notation">is</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#Num.real"><span class="id" title="abbreviation">Num.real</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#55297ec87c6b3f98c14c99daeafb55d3"><span class="id" title="notation">`|</span></a><a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.algebra.ssrnum.html#55297ec87c6b3f98c14c99daeafb55d3"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">||</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_nnormr"><span class="id" title="lemma">lersif_nnormr</span></a> <span class="id" title="var">b</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> 0 <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b3ebd0deddd84fd60e149cb5ef719351"><span class="id" title="notation">~~</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ssrnum.html#55297ec87c6b3f98c14c99daeafb55d3"><span class="id" title="notation">`|</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.algebra.ssrnum.html#55297ec87c6b3f98c14c99daeafb55d3"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#82bf2ea71d9e8bc83fc9c1dc82554e8c"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.interval.html#LersifPo"><span class="id" title="section">LersifPo</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Notation</span> <a name="2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">&quot;</span></a>x &lt;= y ?&lt; 'if' b" := (<a class="idref" href="mathcomp.algebra.interval.html#lersif"><span class="id" title="definition">lersif</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <span class="id" title="var">b</span>)<br/>
+&nbsp;&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 70, <span class="id" title="var">y</span> <span class="id" title="tactic">at</span> <span class="id" title="var">next</span> <span class="id" title="keyword">level</span>,<br/>
+&nbsp;&nbsp;<span class="id" title="var">format</span> "x '[hv'  &lt;=  y '/'  ?&lt;  'if'  b ']'") : <span class="id" title="var">ring_scope</span>.<br/>
+
+<br/>
+<span class="id" title="keyword">Section</span> <a name="LersifOrdered"><span class="id" title="section">LersifOrdered</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Variable</span> (<a name="LersifOrdered.R"><span class="id" title="variable">R</span></a> : <a class="idref" href="mathcomp.algebra.ssrnum.html#Num.RealDomain.Exports.realDomainType"><span class="id" title="abbreviation">realDomainType</span></a>) (<a name="LersifOrdered.b"><span class="id" title="variable">b</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#bool"><span class="id" title="inductive">bool</span></a>) (<a name="LersifOrdered.x"><span class="id" title="variable">x</span></a> <a name="LersifOrdered.y"><span class="id" title="variable">y</span></a> <a name="LersifOrdered.z"><span class="id" title="variable">z</span></a> <a name="LersifOrdered.e"><span class="id" title="variable">e</span></a> : <a class="idref" href="mathcomp.algebra.interval.html#R"><span class="id" title="variable">R</span></a>).<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersifN"><span class="id" title="lemma">lersifN</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b3ebd0deddd84fd60e149cb5ef719351"><span class="id" title="notation">~~</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b3ebd0deddd84fd60e149cb5ef719351"><span class="id" title="notation">~~</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b3ebd0deddd84fd60e149cb5ef719351"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b3ebd0deddd84fd60e149cb5ef719351"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_norml"><span class="id" title="lemma">lersif_norml</span></a> :<br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ssrnum.html#55297ec87c6b3f98c14c99daeafb55d3"><span class="id" title="notation">`|</span></a><a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.algebra.ssrnum.html#55297ec87c6b3f98c14c99daeafb55d3"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&amp;&amp;</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_normr"><span class="id" title="lemma">lersif_normr</span></a> :<br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#55297ec87c6b3f98c14c99daeafb55d3"><span class="id" title="notation">`|</span></a><a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.algebra.ssrnum.html#55297ec87c6b3f98c14c99daeafb55d3"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">||</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_distl"><span class="id" title="lemma">lersif_distl</span></a> :<br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ssrnum.html#55297ec87c6b3f98c14c99daeafb55d3"><span class="id" title="notation">`|</span></a><a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#51dc792c356ca1a71a3094b50d6bb2fb"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.algebra.ssrnum.html#55297ec87c6b3f98c14c99daeafb55d3"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.e"><span class="id" title="variable">e</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#51dc792c356ca1a71a3094b50d6bb2fb"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.e"><span class="id" title="variable">e</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&amp;&amp;</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#c7f78cf1f6a5e4f664654f7d671ca752"><span class="id" title="notation">+</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.e"><span class="id" title="variable">e</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_minr"><span class="id" title="lemma">lersif_minr</span></a> :<br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#Num.min"><span class="id" title="abbreviation">Num.min</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&amp;&amp;</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_minl"><span class="id" title="lemma">lersif_minl</span></a> :<br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ssrnum.html#Num.min"><span class="id" title="abbreviation">Num.min</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">||</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_maxr"><span class="id" title="lemma">lersif_maxr</span></a> :<br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#Num.max"><span class="id" title="abbreviation">Num.max</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">||</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_maxl"><span class="id" title="lemma">lersif_maxl</span></a> :<br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ssrnum.html#Num.max"><span class="id" title="abbreviation">Num.max</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&amp;&amp;</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered.b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.interval.html#LersifOrdered"><span class="id" title="section">LersifOrdered</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Section</span> <a name="LersifField"><span class="id" title="section">LersifField</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Variable</span> (<a name="LersifField.F"><span class="id" title="variable">F</span></a> : <a class="idref" href="mathcomp.algebra.ssrnum.html#Num.NumField.Exports.numFieldType"><span class="id" title="abbreviation">numFieldType</span></a>) (<a name="LersifField.b"><span class="id" title="variable">b</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#bool"><span class="id" title="inductive">bool</span></a>) (<a name="LersifField.z"><span class="id" title="variable">z</span></a> <a name="LersifField.x"><span class="id" title="variable">x</span></a> <a name="LersifField.y"><span class="id" title="variable">y</span></a> : <a class="idref" href="mathcomp.algebra.interval.html#F"><span class="id" title="variable">F</span></a>).<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_pdivl_mulr"><span class="id" title="lemma">lersif_pdivl_mulr</span></a> : 0 <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation">&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.z"><span class="id" title="variable">z</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#69c431a9c94f6f30a655bd7ddb59037b"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#LersifField.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_pdivr_mulr"><span class="id" title="lemma">lersif_pdivr_mulr</span></a> : 0 <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation">&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.z"><span class="id" title="variable">z</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#69c431a9c94f6f30a655bd7ddb59037b"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#LersifField.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_pdivl_mull"><span class="id" title="lemma">lersif_pdivl_mull</span></a> : 0 <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation">&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.z"><span class="id" title="variable">z</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.z"><span class="id" title="variable">z</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#4e5a4c91ec0aa12de06dfe1cc07ea126"><span class="id" title="notation">^-1</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#LersifField.z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_pdivr_mull"><span class="id" title="lemma">lersif_pdivr_mull</span></a> : 0 <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation">&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.z"><span class="id" title="variable">z</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.z"><span class="id" title="variable">z</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#4e5a4c91ec0aa12de06dfe1cc07ea126"><span class="id" title="notation">^-1</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#LersifField.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_ndivl_mulr"><span class="id" title="lemma">lersif_ndivl_mulr</span></a> : <a class="idref" href="mathcomp.algebra.interval.html#LersifField.z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation">&lt;</span></a> 0 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#69c431a9c94f6f30a655bd7ddb59037b"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#LersifField.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_ndivr_mulr"><span class="id" title="lemma">lersif_ndivr_mulr</span></a> : <a class="idref" href="mathcomp.algebra.interval.html#LersifField.z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation">&lt;</span></a> 0 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#69c431a9c94f6f30a655bd7ddb59037b"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#LersifField.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_ndivl_mull"><span class="id" title="lemma">lersif_ndivl_mull</span></a> : <a class="idref" href="mathcomp.algebra.interval.html#LersifField.z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation">&lt;</span></a> 0 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.z"><span class="id" title="variable">z</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#4e5a4c91ec0aa12de06dfe1cc07ea126"><span class="id" title="notation">^-1</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#LersifField.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a><a class="idref" href="mathcomp.algebra.interval.html#LersifField.z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="lersif_ndivr_mull"><span class="id" title="lemma">lersif_ndivr_mull</span></a> : <a class="idref" href="mathcomp.algebra.interval.html#LersifField.z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation">&lt;</span></a> 0 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.z"><span class="id" title="variable">z</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#4e5a4c91ec0aa12de06dfe1cc07ea126"><span class="id" title="notation">^-1</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#LersifField.z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.ssralg.html#2d0cfb150261028f4ebd2ba355623dcc"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#LersifField.b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.interval.html#LersifField"><span class="id" title="section">LersifField</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Variant</span> <a name="itv_bound"><span class="id" title="inductive">itv_bound</span></a> (<span class="id" title="var">T</span> : <span class="id" title="keyword">Type</span>) : <span class="id" title="keyword">Type</span> := <a name="BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <span class="id" title="keyword">of</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#bool"><span class="id" title="inductive">bool</span></a> &amp; <a class="idref" href="mathcomp.algebra.interval.html#T"><span class="id" title="variable">T</span></a> | <a name="BInfty"><span class="id" title="constructor">BInfty</span></a>.<br/>
+<span class="id" title="keyword">Notation</span> <a name="BOpen"><span class="id" title="abbreviation">BOpen</span></a> := (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a>).<br/>
+<span class="id" title="keyword">Notation</span> <a name="BClose"><span class="id" title="abbreviation">BClose</span></a> := (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a>).<br/>
+<span class="id" title="keyword">Variant</span> <a name="interval"><span class="id" title="inductive">interval</span></a> (<span class="id" title="var">T</span> : <span class="id" title="keyword">Type</span>) := <a name="Interval"><span class="id" title="constructor">Interval</span></a> <span class="id" title="keyword">of</span> <a class="idref" href="mathcomp.algebra.interval.html#itv_bound"><span class="id" title="inductive">itv_bound</span></a> <a class="idref" href="mathcomp.algebra.interval.html#T"><span class="id" title="variable">T</span></a> &amp; <a class="idref" href="mathcomp.algebra.interval.html#itv_bound"><span class="id" title="inductive">itv_bound</span></a> <a class="idref" href="mathcomp.algebra.interval.html#T"><span class="id" title="variable">T</span></a>.<br/>
 
 <br/>
 </div>
@@ -109,26 +305,82 @@
  We provide the 9 following notations to help writing formal intervals  
 </div>
 <div class="code">
-<span class="id" title="keyword">Notation</span> <a name="0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">&quot;</span></a>`[ a , b ]" := (<a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BClose"><span class="id" title="abbreviation">BClose</span></a> <span class="id" title="var">a</span>) (<a class="idref" href="mathcomp.algebra.interval.html#BClose"><span class="id" title="abbreviation">BClose</span></a> <span class="id" title="var">b</span>))<br/>
+<span class="id" title="keyword">Notation</span> <a name="3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">&quot;</span></a>`[ a , b ]" := (<a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BClose"><span class="id" title="abbreviation">BClose</span></a> <span class="id" title="var">a</span>) (<a class="idref" href="mathcomp.algebra.interval.html#BClose"><span class="id" title="abbreviation">BClose</span></a> <span class="id" title="var">b</span>))<br/>
 &nbsp;&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">a</span>, <span class="id" title="var">b</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 9 , <span class="id" title="var">format</span> "`[ a ,  b ]") : <span class="id" title="var">ring_scope</span>.<br/>
-<span class="id" title="keyword">Notation</span> <a name="9776a398e1a32aa2aa525fec3dcf7a09"><span class="id" title="notation">&quot;</span></a>`] a , b ]" := (<a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen"><span class="id" title="abbreviation">BOpen</span></a> <span class="id" title="var">a</span>) (<a class="idref" href="mathcomp.algebra.interval.html#BClose"><span class="id" title="abbreviation">BClose</span></a> <span class="id" title="var">b</span>))<br/>
+<span class="id" title="keyword">Notation</span> <a name="9ad860ccdfe75680d287151e25f339b9"><span class="id" title="notation">&quot;</span></a>`] a , b ]" := (<a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen"><span class="id" title="abbreviation">BOpen</span></a> <span class="id" title="var">a</span>) (<a class="idref" href="mathcomp.algebra.interval.html#BClose"><span class="id" title="abbreviation">BClose</span></a> <span class="id" title="var">b</span>))<br/>
 &nbsp;&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">a</span>, <span class="id" title="var">b</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 9 , <span class="id" title="var">format</span> "`] a ,  b ]") : <span class="id" title="var">ring_scope</span>.<br/>
-<span class="id" title="keyword">Notation</span> <a name="e13694bd4c96b2ebd74cba5937d97bac"><span class="id" title="notation">&quot;</span></a>`[ a , b [" := (<a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BClose"><span class="id" title="abbreviation">BClose</span></a> <span class="id" title="var">a</span>) (<a class="idref" href="mathcomp.algebra.interval.html#BOpen"><span class="id" title="abbreviation">BOpen</span></a> <span class="id" title="var">b</span>))<br/>
+<span class="id" title="keyword">Notation</span> <a name="957313378acc4cb77b1d2f647eca85b3"><span class="id" title="notation">&quot;</span></a>`[ a , b [" := (<a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BClose"><span class="id" title="abbreviation">BClose</span></a> <span class="id" title="var">a</span>) (<a class="idref" href="mathcomp.algebra.interval.html#BOpen"><span class="id" title="abbreviation">BOpen</span></a> <span class="id" title="var">b</span>))<br/>
 &nbsp;&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">a</span>, <span class="id" title="var">b</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 9 , <span class="id" title="var">format</span> "`[ a ,  b [") : <span class="id" title="var">ring_scope</span>.<br/>
-<span class="id" title="keyword">Notation</span> <a name="5d6177042cf2728bb3a48ad4d7fef36d"><span class="id" title="notation">&quot;</span></a>`] a , b [" := (<a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen"><span class="id" title="abbreviation">BOpen</span></a> <span class="id" title="var">a</span>) (<a class="idref" href="mathcomp.algebra.interval.html#BOpen"><span class="id" title="abbreviation">BOpen</span></a> <span class="id" title="var">b</span>))<br/>
+<span class="id" title="keyword">Notation</span> <a name="ebff9f8c4fe58806999ff1c12ccee445"><span class="id" title="notation">&quot;</span></a>`] a , b [" := (<a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen"><span class="id" title="abbreviation">BOpen</span></a> <span class="id" title="var">a</span>) (<a class="idref" href="mathcomp.algebra.interval.html#BOpen"><span class="id" title="abbreviation">BOpen</span></a> <span class="id" title="var">b</span>))<br/>
 &nbsp;&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">a</span>, <span class="id" title="var">b</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 9 , <span class="id" title="var">format</span> "`] a ,  b [") : <span class="id" title="var">ring_scope</span>.<br/>
-<span class="id" title="keyword">Notation</span> <a name="6d014c3c0583cf03ab0a7cdc9d80e6e4"><span class="id" title="notation">&quot;</span></a>`] '-oo' , b ]" := (<a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> <span class="id" title="var">_</span>) (<a class="idref" href="mathcomp.algebra.interval.html#BClose"><span class="id" title="abbreviation">BClose</span></a> <span class="id" title="var">b</span>))<br/>
+<span class="id" title="keyword">Notation</span> <a name="f0e10d9b9fd61169852de3c2ca19a38d"><span class="id" title="notation">&quot;</span></a>`] '-oo' , b ]" := (<a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> <span class="id" title="var">_</span>) (<a class="idref" href="mathcomp.algebra.interval.html#BClose"><span class="id" title="abbreviation">BClose</span></a> <span class="id" title="var">b</span>))<br/>
 &nbsp;&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">b</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 9 , <span class="id" title="var">format</span> "`] '-oo' ,  b ]") : <span class="id" title="var">ring_scope</span>.<br/>
-<span class="id" title="keyword">Notation</span> <a name="f7d4545c39e6f558b751e487fae5aef4"><span class="id" title="notation">&quot;</span></a>`] '-oo' , b [" := (<a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> <span class="id" title="var">_</span>) (<a class="idref" href="mathcomp.algebra.interval.html#BOpen"><span class="id" title="abbreviation">BOpen</span></a> <span class="id" title="var">b</span>))<br/>
+<span class="id" title="keyword">Notation</span> <a name="f7d0eaaef362bfb530a5cbf036db1453"><span class="id" title="notation">&quot;</span></a>`] '-oo' , b [" := (<a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> <span class="id" title="var">_</span>) (<a class="idref" href="mathcomp.algebra.interval.html#BOpen"><span class="id" title="abbreviation">BOpen</span></a> <span class="id" title="var">b</span>))<br/>
 &nbsp;&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">b</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 9 , <span class="id" title="var">format</span> "`] '-oo' ,  b [") : <span class="id" title="var">ring_scope</span>.<br/>
-<span class="id" title="keyword">Notation</span> <a name="84c6be04931432ed71a28392cd19d478"><span class="id" title="notation">&quot;</span></a>`[ a , '+oo' [" := (<a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BClose"><span class="id" title="abbreviation">BClose</span></a> <span class="id" title="var">a</span>) (<a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> <span class="id" title="var">_</span>))<br/>
+<span class="id" title="keyword">Notation</span> <a name="c5d1424554ae4f6d783beb7e2b68e8c1"><span class="id" title="notation">&quot;</span></a>`[ a , '+oo' [" := (<a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BClose"><span class="id" title="abbreviation">BClose</span></a> <span class="id" title="var">a</span>) (<a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> <span class="id" title="var">_</span>))<br/>
 &nbsp;&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">a</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 9 , <span class="id" title="var">format</span> "`[ a ,  '+oo' [") : <span class="id" title="var">ring_scope</span>.<br/>
-<span class="id" title="keyword">Notation</span> <a name="ddab974cd5332360c70b1aca114bd394"><span class="id" title="notation">&quot;</span></a>`] a , '+oo' [" := (<a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen"><span class="id" title="abbreviation">BOpen</span></a> <span class="id" title="var">a</span>) (<a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> <span class="id" title="var">_</span>))<br/>
+<span class="id" title="keyword">Notation</span> <a name="1133a1612ce44fa1571c2c531aeb13a2"><span class="id" title="notation">&quot;</span></a>`] a , '+oo' [" := (<a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen"><span class="id" title="abbreviation">BOpen</span></a> <span class="id" title="var">a</span>) (<a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> <span class="id" title="var">_</span>))<br/>
 &nbsp;&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">a</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 9 , <span class="id" title="var">format</span> "`] a ,  '+oo' [") : <span class="id" title="var">ring_scope</span>.<br/>
-<span class="id" title="keyword">Notation</span> <a name="996170680ea33f9a35c3d01667d531c3"><span class="id" title="notation">&quot;</span></a>`] -oo , '+oo' [" := (<a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> <span class="id" title="var">_</span>) (<a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> <span class="id" title="var">_</span>))<br/>
+<span class="id" title="keyword">Notation</span> <a name="2d0f4f3a8486d97a7c68fd4d2f96ccac"><span class="id" title="notation">&quot;</span></a>`] -oo , '+oo' [" := (<a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> <span class="id" title="var">_</span>) (<a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> <span class="id" title="var">_</span>))<br/>
 &nbsp;&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "`] -oo ,  '+oo' [") : <span class="id" title="var">ring_scope</span>.<br/>
 
 <br/>
+<span class="id" title="keyword">Section</span> <a name="IntervalEq"><span class="id" title="section">IntervalEq</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Variable</span> <a name="IntervalEq.T"><span class="id" title="variable">T</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Exports.eqType"><span class="id" title="abbreviation">eqType</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="eq_itv_bound"><span class="id" title="definition">eq_itv_bound</span></a> (<span class="id" title="var">b1</span> <span class="id" title="var">b2</span> : <a class="idref" href="mathcomp.algebra.interval.html#itv_bound"><span class="id" title="inductive">itv_bound</span></a> <a class="idref" href="mathcomp.algebra.interval.html#IntervalEq.T"><span class="id" title="variable">T</span></a>) : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#bool"><span class="id" title="inductive">bool</span></a> :=<br/>
+&nbsp;&nbsp;<span class="id" title="keyword">match</span> <a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a>, <a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a> <span class="id" title="keyword">with</span><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;| <a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <span class="id" title="var">a</span> <span class="id" title="var">x</span>, <a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <span class="id" title="var">b</span> <span class="id" title="var">y</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <span class="id" title="var">b</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&amp;&amp;</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <span class="id" title="var">y</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;| <a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a>, <a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;| <span class="id" title="var">_</span>, <span class="id" title="var">_</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a><br/>
+&nbsp;&nbsp;<span class="id" title="keyword">end</span>.<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="eq_itv_boundP"><span class="id" title="lemma">eq_itv_boundP</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.axiom"><span class="id" title="definition">Equality.axiom</span></a> <a class="idref" href="mathcomp.algebra.interval.html#eq_itv_bound"><span class="id" title="definition">eq_itv_bound</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Canonical</span> <span class="id" title="var">itv_bound_eqMixin</span> := <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Exports.EqMixin"><span class="id" title="abbreviation">EqMixin</span></a> <a class="idref" href="mathcomp.algebra.interval.html#eq_itv_boundP"><span class="id" title="lemma">eq_itv_boundP</span></a>.<br/>
+<span class="id" title="keyword">Canonical</span> <span class="id" title="var">itv_bound_eqType</span> :=<br/>
+&nbsp;&nbsp;<span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Exports.EqType"><span class="id" title="abbreviation">EqType</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#itv_bound"><span class="id" title="inductive">itv_bound</span></a> <a class="idref" href="mathcomp.algebra.interval.html#IntervalEq.T"><span class="id" title="variable">T</span></a>) <a class="idref" href="mathcomp.algebra.interval.html#itv_bound_eqMixin"><span class="id" title="definition">itv_bound_eqMixin</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="eqitv"><span class="id" title="definition">eqitv</span></a> (<span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.algebra.interval.html#interval"><span class="id" title="inductive">interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#IntervalEq.T"><span class="id" title="variable">T</span></a>) : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#bool"><span class="id" title="inductive">bool</span></a> :=<br/>
+&nbsp;&nbsp;<span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <span class="id" title="var">x</span> <span class="id" title="var">x'</span> := <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <span class="id" title="tactic">in</span><br/>
+&nbsp;&nbsp;<span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <span class="id" title="var">y</span> <span class="id" title="var">y'</span> := <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <span class="id" title="tactic">in</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&amp;&amp;</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><span class="id" title="var">x'</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <span class="id" title="var">y'</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="eqitvP"><span class="id" title="lemma">eqitvP</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.axiom"><span class="id" title="definition">Equality.axiom</span></a> <a class="idref" href="mathcomp.algebra.interval.html#eqitv"><span class="id" title="definition">eqitv</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Canonical</span> <span class="id" title="var">interval_eqMixin</span> := <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Exports.EqMixin"><span class="id" title="abbreviation">EqMixin</span></a> <a class="idref" href="mathcomp.algebra.interval.html#eqitvP"><span class="id" title="lemma">eqitvP</span></a>.<br/>
+<span class="id" title="keyword">Canonical</span> <span class="id" title="var">interval_eqType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Exports.EqType"><span class="id" title="abbreviation">EqType</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#interval"><span class="id" title="inductive">interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#IntervalEq.T"><span class="id" title="variable">T</span></a>) <a class="idref" href="mathcomp.algebra.interval.html#interval_eqMixin"><span class="id" title="definition">interval_eqMixin</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.interval.html#IntervalEq"><span class="id" title="section">IntervalEq</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Section</span> <a name="IntervalPo"><span class="id" title="section">IntervalPo</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Variable</span> <a name="IntervalPo.R"><span class="id" title="variable">R</span></a> : <a class="idref" href="mathcomp.algebra.ssrnum.html#Num.NumDomain.Exports.numDomainType"><span class="id" title="abbreviation">numDomainType</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="pred_of_itv"><span class="id" title="definition">pred_of_itv</span></a> (<span class="id" title="var">i</span> : <a class="idref" href="mathcomp.algebra.interval.html#interval"><span class="id" title="inductive">interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>) : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a> :=<br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#27dabc72ea2c2c768f2db80a79f42524"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#27dabc72ea2c2c768f2db80a79f42524"><span class="id" title="notation">pred</span></a> <span class="id" title="var">x</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#27dabc72ea2c2c768f2db80a79f42524"><span class="id" title="notation">|</span></a> <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <span class="id" title="var">l</span> <span class="id" title="var">u</span> := <a class="idref" href="mathcomp.algebra.interval.html#i"><span class="id" title="variable">i</span></a> <span class="id" title="tactic">in</span><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="id" title="keyword">match</span> <span class="id" title="var">l</span> <span class="id" title="keyword">with</span><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| <a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <span class="id" title="var">b</span> <span class="id" title="var">lb</span> ⇒ <span class="id" title="var">lb</span> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <span class="id" title="var">b</span><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| <a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="id" title="keyword">end</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&amp;&amp;</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="id" title="keyword">match</span> <span class="id" title="var">u</span> <span class="id" title="keyword">with</span><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| <a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <span class="id" title="var">b</span> <span class="id" title="var">ub</span> ⇒ <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <span class="id" title="var">ub</span> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <span class="id" title="var">b</span><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| <a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="id" title="keyword">end</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#27dabc72ea2c2c768f2db80a79f42524"><span class="id" title="notation">]</span></a>.<br/>
+<span class="id" title="keyword">Canonical</span> <span class="id" title="keyword">Structure</span> <span class="id" title="var">itvPredType</span> := <a class="idref" href="mathcomp.ssreflect.ssrbool.html#PredType"><span class="id" title="definition">PredType</span></a> <a class="idref" href="mathcomp.algebra.interval.html#pred_of_itv"><span class="id" title="definition">pred_of_itv</span></a>.<br/>
+
+<br/>
 </div>
 
 <div class="doc">
@@ -138,258 +390,242 @@
 <span class="id" title="keyword">Definition</span> <a name="itv_rewrite"><span class="id" title="definition">itv_rewrite</span></a> (<span class="id" title="var">i</span> : <a class="idref" href="mathcomp.algebra.interval.html#interval"><span class="id" title="inductive">interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>) <span class="id" title="var">x</span> : <span class="id" title="keyword">Type</span> :=<br/>
 &nbsp;&nbsp;<span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <span class="id" title="var">l</span> <span class="id" title="var">u</span> := <a class="idref" href="mathcomp.algebra.interval.html#i"><span class="id" title="variable">i</span></a> <span class="id" title="tactic">in</span><br/>
 &nbsp;&nbsp;&nbsp;&nbsp;(<span class="id" title="keyword">match</span> <span class="id" title="var">l</span> <span class="id" title="keyword">with</span><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| <span class="id" title="var">BClose</span> <span class="id" title="var">a</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#1065783963a393d1eafa2137291f2495"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#388c172bf8d34ef0bf11898cd56f8d7b"><span class="id" title="notation">&lt;</span></a> <span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| <span class="id" title="var">BOpen</span> <span class="id" title="var">a</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#1065783963a393d1eafa2137291f2495"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#388c172bf8d34ef0bf11898cd56f8d7b"><span class="id" title="notation">&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#1065783963a393d1eafa2137291f2495"><span class="id" title="notation">≤</span></a> <span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| <a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> ⇒ <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>, <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="id" title="keyword">end</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| <span class="id" title="var">BClose</span> <span class="id" title="var">a</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#cb42ec59ad57b25928e1718b4e69e031"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation">&lt;</span></a> <span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| <span class="id" title="var">BOpen</span> <span class="id" title="var">a</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#cb42ec59ad57b25928e1718b4e69e031"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation">&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#cb42ec59ad57b25928e1718b4e69e031"><span class="id" title="notation">≤</span></a> <span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation">&lt;</span></a> <span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| <a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> ⇒ <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>, <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="id" title="keyword">end</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a><br/>
 &nbsp;&nbsp;&nbsp;&nbsp;<span class="id" title="keyword">match</span> <span class="id" title="var">u</span> <span class="id" title="keyword">with</span><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| <span class="id" title="var">BClose</span> <span class="id" title="var">b</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#1065783963a393d1eafa2137291f2495"><span class="id" title="notation">≤</span></a> <span class="id" title="var">b</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><span class="id" title="var">b</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#388c172bf8d34ef0bf11898cd56f8d7b"><span class="id" title="notation">&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| <span class="id" title="var">BOpen</span> <span class="id" title="var">b</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#1065783963a393d1eafa2137291f2495"><span class="id" title="notation">≤</span></a> <span class="id" title="var">b</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#388c172bf8d34ef0bf11898cd56f8d7b"><span class="id" title="notation">&lt;</span></a> <span class="id" title="var">b</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><span class="id" title="var">b</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#1065783963a393d1eafa2137291f2495"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| <a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> ⇒ <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>, <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="id" title="keyword">end</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| <span class="id" title="var">BClose</span> <span class="id" title="var">b</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#cb42ec59ad57b25928e1718b4e69e031"><span class="id" title="notation">≤</span></a> <span class="id" title="var">b</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">b</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation">&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| <span class="id" title="var">BOpen</span> <span class="id" title="var">b</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#cb42ec59ad57b25928e1718b4e69e031"><span class="id" title="notation">≤</span></a> <span class="id" title="var">b</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation">&lt;</span></a> <span class="id" title="var">b</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">b</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#cb42ec59ad57b25928e1718b4e69e031"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">b</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation">&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| <a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> ⇒ <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>, <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="id" title="keyword">end</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a><br/>
 &nbsp;&nbsp;&nbsp;&nbsp;<span class="id" title="keyword">match</span> <span class="id" title="var">l</span>, <span class="id" title="var">u</span> <span class="id" title="keyword">with</span><br/>
 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| <span class="id" title="var">BClose</span> <span class="id" title="var">a</span>, <span class="id" title="var">BClose</span> <span class="id" title="var">b</span> ⇒<br/>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#1065783963a393d1eafa2137291f2495"><span class="id" title="notation">≤</span></a> <span class="id" title="var">b</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><span class="id" title="var">b</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#388c172bf8d34ef0bf11898cd56f8d7b"><span class="id" title="notation">&lt;</span></a> <span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">`[</span></a><span class="id" title="var">a</span><a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">,</span></a> <span class="id" title="var">b</span><a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><span class="id" title="var">b</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">`[</span></a><span class="id" title="var">a</span><a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">,</span></a> <span class="id" title="var">b</span><a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#cb42ec59ad57b25928e1718b4e69e031"><span class="id" title="notation">≤</span></a> <span class="id" title="var">b</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">b</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation">&lt;</span></a> <span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">`[</span></a><span class="id" title="var">a</span><a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">,</span></a> <span class="id" title="var">b</span><a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">b</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">`[</span></a><span class="id" title="var">a</span><a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">,</span></a> <span class="id" title="var">b</span><a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a><br/>
 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| <span class="id" title="var">BClose</span> <span class="id" title="var">a</span>, <span class="id" title="var">BOpen</span> <span class="id" title="var">b</span> ⇒<br/>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#1065783963a393d1eafa2137291f2495"><span class="id" title="notation">≤</span></a> <span class="id" title="var">b</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#388c172bf8d34ef0bf11898cd56f8d7b"><span class="id" title="notation">&lt;</span></a> <span class="id" title="var">b</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><span class="id" title="var">b</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#1065783963a393d1eafa2137291f2495"><span class="id" title="notation">≤</span></a> <span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">`[</span></a><span class="id" title="var">a</span><a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">,</span></a> <span class="id" title="var">b</span><a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#e13694bd4c96b2ebd74cba5937d97bac"><span class="id" title="notation">`[</span></a><span class="id" title="var">a</span><a class="idref" href="mathcomp.algebra.interval.html#e13694bd4c96b2ebd74cba5937d97bac"><span class="id" title="notation">,</span></a> <span class="id" title="var">b</span><a class="idref" href="mathcomp.algebra.interval.html#e13694bd4c96b2ebd74cba5937d97bac"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)*</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><span class="id" title="var">b</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">`[</span></a><span class="id" title="var">a</span><a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">,</span></a> <span class="id" title="var">b</span><a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><span class="id" title="var">b</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#9776a398e1a32aa2aa525fec3dcf7a09"><span class="id" title="notation">`]</span></a><span class="id" title="var">a</span><a class="idref" href="mathcomp.algebra.interval.html#9776a398e1a32aa2aa525fec3dcf7a09"><span class="id" title="notation">,</span></a> <span class="id" title="var">b</span><a class="idref" href="mathcomp.algebra.interval.html#9776a398e1a32aa2aa525fec3dcf7a09"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#cb42ec59ad57b25928e1718b4e69e031"><span class="id" title="notation">≤</span></a> <span class="id" title="var">b</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation">&lt;</span></a> <span class="id" title="var">b</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">b</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#cb42ec59ad57b25928e1718b4e69e031"><span class="id" title="notation">≤</span></a> <span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">b</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation">&lt;</span></a> <span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">`[</span></a><span class="id" title="var">a</span><a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">,</span></a> <span class="id" title="var">b</span><a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#957313378acc4cb77b1d2f647eca85b3"><span class="id" title="notation">`[</span></a><span class="id" title="var">a</span><a class="idref" href="mathcomp.algebra.interval.html#957313378acc4cb77b1d2f647eca85b3"><span class="id" title="notation">,</span></a> <span class="id" title="var">b</span><a class="idref" href="mathcomp.algebra.interval.html#957313378acc4cb77b1d2f647eca85b3"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)*</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">b</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">`[</span></a><span class="id" title="var">a</span><a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">,</span></a> <span class="id" title="var">b</span><a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">b</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#9ad860ccdfe75680d287151e25f339b9"><span class="id" title="notation">`]</span></a><span class="id" title="var">a</span><a class="idref" href="mathcomp.algebra.interval.html#9ad860ccdfe75680d287151e25f339b9"><span class="id" title="notation">,</span></a> <span class="id" title="var">b</span><a class="idref" href="mathcomp.algebra.interval.html#9ad860ccdfe75680d287151e25f339b9"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a><br/>
 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| <span class="id" title="var">BOpen</span> <span class="id" title="var">a</span>, <span class="id" title="var">BClose</span> <span class="id" title="var">b</span> ⇒<br/>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#1065783963a393d1eafa2137291f2495"><span class="id" title="notation">≤</span></a> <span class="id" title="var">b</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#388c172bf8d34ef0bf11898cd56f8d7b"><span class="id" title="notation">&lt;</span></a> <span class="id" title="var">b</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><span class="id" title="var">b</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#1065783963a393d1eafa2137291f2495"><span class="id" title="notation">≤</span></a> <span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">`[</span></a><span class="id" title="var">a</span><a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">,</span></a> <span class="id" title="var">b</span><a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#e13694bd4c96b2ebd74cba5937d97bac"><span class="id" title="notation">`[</span></a><span class="id" title="var">a</span><a class="idref" href="mathcomp.algebra.interval.html#e13694bd4c96b2ebd74cba5937d97bac"><span class="id" title="notation">,</span></a> <span class="id" title="var">b</span><a class="idref" href="mathcomp.algebra.interval.html#e13694bd4c96b2ebd74cba5937d97bac"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)*</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><span class="id" title="var">b</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">`[</span></a><span class="id" title="var">a</span><a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">,</span></a> <span class="id" title="var">b</span><a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><span class="id" title="var">b</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#9776a398e1a32aa2aa525fec3dcf7a09"><span class="id" title="notation">`]</span></a><span class="id" title="var">a</span><a class="idref" href="mathcomp.algebra.interval.html#9776a398e1a32aa2aa525fec3dcf7a09"><span class="id" title="notation">,</span></a> <span class="id" title="var">b</span><a class="idref" href="mathcomp.algebra.interval.html#9776a398e1a32aa2aa525fec3dcf7a09"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#cb42ec59ad57b25928e1718b4e69e031"><span class="id" title="notation">≤</span></a> <span class="id" title="var">b</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation">&lt;</span></a> <span class="id" title="var">b</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">b</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#cb42ec59ad57b25928e1718b4e69e031"><span class="id" title="notation">≤</span></a> <span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">b</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation">&lt;</span></a> <span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">`[</span></a><span class="id" title="var">a</span><a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">,</span></a> <span class="id" title="var">b</span><a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#957313378acc4cb77b1d2f647eca85b3"><span class="id" title="notation">`[</span></a><span class="id" title="var">a</span><a class="idref" href="mathcomp.algebra.interval.html#957313378acc4cb77b1d2f647eca85b3"><span class="id" title="notation">,</span></a> <span class="id" title="var">b</span><a class="idref" href="mathcomp.algebra.interval.html#957313378acc4cb77b1d2f647eca85b3"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)*</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">b</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">`[</span></a><span class="id" title="var">a</span><a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">,</span></a> <span class="id" title="var">b</span><a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">b</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#9ad860ccdfe75680d287151e25f339b9"><span class="id" title="notation">`]</span></a><span class="id" title="var">a</span><a class="idref" href="mathcomp.algebra.interval.html#9ad860ccdfe75680d287151e25f339b9"><span class="id" title="notation">,</span></a> <span class="id" title="var">b</span><a class="idref" href="mathcomp.algebra.interval.html#9ad860ccdfe75680d287151e25f339b9"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a><br/>
 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| <span class="id" title="var">BOpen</span> <span class="id" title="var">a</span>, <span class="id" title="var">BOpen</span> <span class="id" title="var">b</span> ⇒<br/>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#1065783963a393d1eafa2137291f2495"><span class="id" title="notation">≤</span></a> <span class="id" title="var">b</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#388c172bf8d34ef0bf11898cd56f8d7b"><span class="id" title="notation">&lt;</span></a> <span class="id" title="var">b</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><span class="id" title="var">b</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#1065783963a393d1eafa2137291f2495"><span class="id" title="notation">≤</span></a> <span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">`[</span></a><span class="id" title="var">a</span><a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">,</span></a> <span class="id" title="var">b</span><a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#e13694bd4c96b2ebd74cba5937d97bac"><span class="id" title="notation">`[</span></a><span class="id" title="var">a</span><a class="idref" href="mathcomp.algebra.interval.html#e13694bd4c96b2ebd74cba5937d97bac"><span class="id" title="notation">,</span></a> <span class="id" title="var">b</span><a class="idref" href="mathcomp.algebra.interval.html#e13694bd4c96b2ebd74cba5937d97bac"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)*</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><span class="id" title="var">b</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">`[</span></a><span class="id" title="var">a</span><a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">,</span></a> <span class="id" title="var">b</span><a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><span class="id" title="var">b</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#9776a398e1a32aa2aa525fec3dcf7a09"><span class="id" title="notation">`]</span></a><span class="id" title="var">a</span><a class="idref" href="mathcomp.algebra.interval.html#9776a398e1a32aa2aa525fec3dcf7a09"><span class="id" title="notation">,</span></a> <span class="id" title="var">b</span><a class="idref" href="mathcomp.algebra.interval.html#9776a398e1a32aa2aa525fec3dcf7a09"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| <span class="id" title="var">_</span>, <span class="id" title="var">_</span> ⇒ <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>, <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#cb42ec59ad57b25928e1718b4e69e031"><span class="id" title="notation">≤</span></a> <span class="id" title="var">b</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation">&lt;</span></a> <span class="id" title="var">b</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">b</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#cb42ec59ad57b25928e1718b4e69e031"><span class="id" title="notation">≤</span></a> <span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">b</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation">&lt;</span></a> <span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">`[</span></a><span class="id" title="var">a</span><a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">,</span></a> <span class="id" title="var">b</span><a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#957313378acc4cb77b1d2f647eca85b3"><span class="id" title="notation">`[</span></a><span class="id" title="var">a</span><a class="idref" href="mathcomp.algebra.interval.html#957313378acc4cb77b1d2f647eca85b3"><span class="id" title="notation">,</span></a> <span class="id" title="var">b</span><a class="idref" href="mathcomp.algebra.interval.html#957313378acc4cb77b1d2f647eca85b3"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)*</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">b</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">`[</span></a><span class="id" title="var">a</span><a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">,</span></a> <span class="id" title="var">b</span><a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="var">b</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#9ad860ccdfe75680d287151e25f339b9"><span class="id" title="notation">`]</span></a><span class="id" title="var">a</span><a class="idref" href="mathcomp.algebra.interval.html#9ad860ccdfe75680d287151e25f339b9"><span class="id" title="notation">,</span></a> <span class="id" title="var">b</span><a class="idref" href="mathcomp.algebra.interval.html#9ad860ccdfe75680d287151e25f339b9"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| <span class="id" title="var">_</span>, <span class="id" title="var">_</span> ⇒ <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>, <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a><br/>
 &nbsp;&nbsp;&nbsp;&nbsp;<span class="id" title="keyword">end</span>)%<span class="id" title="keyword">type</span>.<br/>
 
 <br/>
 <span class="id" title="keyword">Definition</span> <a name="itv_decompose"><span class="id" title="definition">itv_decompose</span></a> (<span class="id" title="var">i</span> : <a class="idref" href="mathcomp.algebra.interval.html#interval"><span class="id" title="inductive">interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>) <span class="id" title="var">x</span> : <span class="id" title="keyword">Prop</span> :=<br/>
 &nbsp;&nbsp;<span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <span class="id" title="var">l</span> <span class="id" title="var">u</span> := <a class="idref" href="mathcomp.algebra.interval.html#i"><span class="id" title="variable">i</span></a> <span class="id" title="tactic">in</span><br/>
-&nbsp;&nbsp;(<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><span class="id" title="keyword">match</span> <span class="id" title="var">l</span> <span class="id" title="keyword">with</span><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;| <span class="id" title="var">BClose</span> <span class="id" title="var">a</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0fffdc558ce71ab561d36c8a8094dbe5"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#1065783963a393d1eafa2137291f2495"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0fffdc558ce71ab561d36c8a8094dbe5"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0fffdc558ce71ab561d36c8a8094dbe5"><span class="id" title="notation">:</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0fffdc558ce71ab561d36c8a8094dbe5"><span class="id" title="notation">Prop</span></a><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;| <span class="id" title="var">BOpen</span> <span class="id" title="var">a</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0fffdc558ce71ab561d36c8a8094dbe5"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="mathcomp.algebra.ssrnum.html#388c172bf8d34ef0bf11898cd56f8d7b"><span class="id" title="notation">&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0fffdc558ce71ab561d36c8a8094dbe5"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0fffdc558ce71ab561d36c8a8094dbe5"><span class="id" title="notation">:</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0fffdc558ce71ab561d36c8a8094dbe5"><span class="id" title="notation">Prop</span></a><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;| <a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#True"><span class="id" title="inductive">True</span></a><br/>
-&nbsp;&nbsp;<span class="id" title="keyword">end</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0fffdc558ce71ab561d36c8a8094dbe5"><span class="id" title="notation">:</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0fffdc558ce71ab561d36c8a8094dbe5"><span class="id" title="notation">Prop</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">×</span></a><br/>
-&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">(</span></a><span class="id" title="keyword">match</span> <span class="id" title="var">u</span> <span class="id" title="keyword">with</span><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;| <span class="id" title="var">BClose</span> <span class="id" title="var">b</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0fffdc558ce71ab561d36c8a8094dbe5"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#1065783963a393d1eafa2137291f2495"><span class="id" title="notation">≤</span></a> <span class="id" title="var">b</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0fffdc558ce71ab561d36c8a8094dbe5"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0fffdc558ce71ab561d36c8a8094dbe5"><span class="id" title="notation">:</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0fffdc558ce71ab561d36c8a8094dbe5"><span class="id" title="notation">Prop</span></a><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;| <span class="id" title="var">BOpen</span> <span class="id" title="var">b</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0fffdc558ce71ab561d36c8a8094dbe5"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#388c172bf8d34ef0bf11898cd56f8d7b"><span class="id" title="notation">&lt;</span></a> <span class="id" title="var">b</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0fffdc558ce71ab561d36c8a8094dbe5"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0fffdc558ce71ab561d36c8a8094dbe5"><span class="id" title="notation">:</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0fffdc558ce71ab561d36c8a8094dbe5"><span class="id" title="notation">Prop</span></a><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;| <a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#True"><span class="id" title="inductive">True</span></a><br/>
-&nbsp;&nbsp;<span class="id" title="keyword">end</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0fffdc558ce71ab561d36c8a8094dbe5"><span class="id" title="notation">:</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0fffdc558ce71ab561d36c8a8094dbe5"><span class="id" title="notation">Prop</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#d19c7eafd0e2d195d10df94b392087b5"><span class="id" title="notation">)</span></a>)%<span class="id" title="keyword">type</span>.<br/>
+&nbsp;&nbsp;(<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="keyword">match</span> <span class="id" title="var">l</span> <span class="id" title="keyword">with</span><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;| <a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <span class="id" title="var">b</span> <span class="id" title="var">lb</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#17ff6c89d595412214a9dd9e39474c36"><span class="id" title="notation">(</span></a><span class="id" title="var">lb</span> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <span class="id" title="var">b</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#17ff6c89d595412214a9dd9e39474c36"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#17ff6c89d595412214a9dd9e39474c36"><span class="id" title="notation">:</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#17ff6c89d595412214a9dd9e39474c36"><span class="id" title="notation">Prop</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;| <a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#True"><span class="id" title="inductive">True</span></a><br/>
+&nbsp;&nbsp;<span class="id" title="keyword">end</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#17ff6c89d595412214a9dd9e39474c36"><span class="id" title="notation">:</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#17ff6c89d595412214a9dd9e39474c36"><span class="id" title="notation">Prop</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a><br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">(</span></a><span class="id" title="keyword">match</span> <span class="id" title="var">u</span> <span class="id" title="keyword">with</span><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;| <a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <span class="id" title="var">b</span> <span class="id" title="var">ub</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#17ff6c89d595412214a9dd9e39474c36"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <span class="id" title="var">ub</span> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <span class="id" title="var">b</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#17ff6c89d595412214a9dd9e39474c36"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#17ff6c89d595412214a9dd9e39474c36"><span class="id" title="notation">:</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#17ff6c89d595412214a9dd9e39474c36"><span class="id" title="notation">Prop</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;| <a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#True"><span class="id" title="inductive">True</span></a><br/>
+&nbsp;&nbsp;<span class="id" title="keyword">end</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#17ff6c89d595412214a9dd9e39474c36"><span class="id" title="notation">:</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#17ff6c89d595412214a9dd9e39474c36"><span class="id" title="notation">Prop</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">)</span></a>)%<span class="id" title="keyword">type</span>.<br/>
 
 <br/>
 <span class="id" title="keyword">Lemma</span> <a name="itv_dec"><span class="id" title="lemma">itv_dec</span></a> : <span class="id" title="keyword">∀</span> (<span class="id" title="var">x</span> : <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>) (<span class="id" title="var">i</span> : <a class="idref" href="mathcomp.algebra.interval.html#interval"><span class="id" title="inductive">interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>),<br/>
-&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#itv_decompose"><span class="id" title="definition">itv_decompose</span></a> <a class="idref" href="mathcomp.algebra.interval.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a>) (<a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#i"><span class="id" title="variable">i</span></a>).<br/>
- 
-<br/>
-
-<br/>
-<span class="id" title="keyword">Definition</span> <a name="lersif"><span class="id" title="definition">lersif</span></a> (<span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>) <span class="id" title="var">b</span> := <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">then</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#388c172bf8d34ef0bf11898cd56f8d7b"><span class="id" title="notation">&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">else</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#1065783963a393d1eafa2137291f2495"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a>.<br/>
-
-<br/>
-
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="lersifxx"><span class="id" title="lemma">lersifxx</span></a> <span class="id" title="var">x</span> <span class="id" title="var">b</span>: <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#4b80c70cdb231351c5e129ba61f7f956"><span class="id" title="notation">~~</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a>.<br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#itv_decompose"><span class="id" title="definition">itv_decompose</span></a> <a class="idref" href="mathcomp.algebra.interval.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a>) (<a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#i"><span class="id" title="variable">i</span></a>).<br/>
  
 <br/>
-<span class="id" title="keyword">Lemma</span> <a name="lersif_trans"><span class="id" title="lemma">lersif_trans</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <span class="id" title="var">z</span> <span class="id" title="var">b1</span> <span class="id" title="var">b2</span> :<br/>
-&nbsp;&nbsp;<a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#14a7a9c7dc61f86bfb664d400fabaf8a"><span class="id" title="notation">||</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a>.<br/>
 
 <br/>
-<span class="id" title="keyword">Lemma</span> <a name="lersifW"><span class="id" title="lemma">lersifW</span></a> <span class="id" title="var">b</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#1065783963a393d1eafa2137291f2495"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a>.<br/>
- 
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="lersifNF"><span class="id" title="lemma">lersifNF</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <span class="id" title="var">b</span> : <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">if</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#4b80c70cdb231351c5e129ba61f7f956"><span class="id" title="notation">~~</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a>  <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a>.<br/>
- 
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="lersifS"><span class="id" title="lemma">lersifS</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <span class="id" title="var">b</span> : <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#388c172bf8d34ef0bf11898cd56f8d7b"><span class="id" title="notation">&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a>.<br/>
- 
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="lersifT"><span class="id" title="lemma">lersifT</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">if</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#388c172bf8d34ef0bf11898cd56f8d7b"><span class="id" title="notation">&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.  <br/>
-
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="lersifF"><span class="id" title="lemma">lersifF</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">if</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#1065783963a393d1eafa2137291f2495"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.  <br/>
-
-<br/>
-<span class="id" title="keyword">Definition</span> <a name="le_boundl"><span class="id" title="definition">le_boundl</span></a> <span class="id" title="var">b1</span> <span class="id" title="var">b2</span> :=<br/>
+<span class="id" title="keyword">Definition</span> <a name="le_boundl"><span class="id" title="definition">le_boundl</span></a> (<span class="id" title="var">b1</span> <span class="id" title="var">b2</span> : <a class="idref" href="mathcomp.algebra.interval.html#itv_bound"><span class="id" title="inductive">itv_bound</span></a> <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>) :=<br/>
 &nbsp;&nbsp;<span class="id" title="keyword">match</span> <a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a>, <a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a> <span class="id" title="keyword">with</span><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;| <a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <span class="id" title="var">b1</span> <span class="id" title="var">x1</span>, <a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <span class="id" title="var">b2</span> <span class="id" title="var">x2</span> ⇒ <span class="id" title="var">x1</span> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">≤</span></a> <span class="id" title="var">x2</span> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">(</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#4b80c70cdb231351c5e129ba61f7f956"><span class="id" title="notation">~~</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&amp;&amp;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a><a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">)</span></a><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;| <a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span>, <a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;| <span class="id" title="var">_</span>, <span class="id" title="var">_</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;| <a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <span class="id" title="var">b1</span> <span class="id" title="var">x1</span>, <a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <span class="id" title="var">b2</span> <span class="id" title="var">x2</span> ⇒ <span class="id" title="var">x1</span> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <span class="id" title="var">x2</span> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b3ebd0deddd84fd60e149cb5ef719351"><span class="id" title="notation">~~</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&amp;&amp;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;| <a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span>, <a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;| <span class="id" title="var">_</span>, <span class="id" title="var">_</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a><br/>
 &nbsp;&nbsp;<span class="id" title="keyword">end</span>.<br/>
 
 <br/>
-<span class="id" title="keyword">Definition</span> <a name="le_boundr"><span class="id" title="definition">le_boundr</span></a> <span class="id" title="var">b1</span> <span class="id" title="var">b2</span> :=<br/>
+<span class="id" title="keyword">Definition</span> <a name="le_boundr"><span class="id" title="definition">le_boundr</span></a> (<span class="id" title="var">b1</span> <span class="id" title="var">b2</span> : <a class="idref" href="mathcomp.algebra.interval.html#itv_bound"><span class="id" title="inductive">itv_bound</span></a> <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>) :=<br/>
 &nbsp;&nbsp;<span class="id" title="keyword">match</span> <a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a>, <a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a> <span class="id" title="keyword">with</span><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;| <a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <span class="id" title="var">b1</span> <span class="id" title="var">x1</span>, <a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <span class="id" title="var">b2</span> <span class="id" title="var">x2</span> ⇒ <span class="id" title="var">x1</span> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">≤</span></a> <span class="id" title="var">x2</span> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">(</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#4b80c70cdb231351c5e129ba61f7f956"><span class="id" title="notation">~~</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&amp;&amp;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a><a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">)</span></a><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;| <a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a>, <a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;| <span class="id" title="var">_</span>, <span class="id" title="var">_</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;| <a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <span class="id" title="var">b1</span> <span class="id" title="var">x1</span>, <a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <span class="id" title="var">b2</span> <span class="id" title="var">x2</span> ⇒ <span class="id" title="var">x1</span> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <span class="id" title="var">x2</span> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b3ebd0deddd84fd60e149cb5ef719351"><span class="id" title="notation">~~</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&amp;&amp;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;| <a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a>, <a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;| <span class="id" title="var">_</span>, <span class="id" title="var">_</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a><br/>
 &nbsp;&nbsp;<span class="id" title="keyword">end</span>.<br/>
 
 <br/>
 <span class="id" title="keyword">Lemma</span> <a name="itv_boundlr"><span class="id" title="lemma">itv_boundlr</span></a> <span class="id" title="var">bl</span> <span class="id" title="var">br</span> <span class="id" title="var">x</span> :<br/>
-&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bl"><span class="id" title="variable">bl</span></a> <a class="idref" href="mathcomp.algebra.interval.html#br"><span class="id" title="variable">br</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a><br/>
-&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#le_boundl"><span class="id" title="definition">le_boundl</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bl"><span class="id" title="variable">bl</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BClose"><span class="id" title="abbreviation">BClose</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&amp;&amp;</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#le_boundr"><span class="id" title="definition">le_boundr</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BClose"><span class="id" title="abbreviation">BClose</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a>) <a class="idref" href="mathcomp.algebra.interval.html#br"><span class="id" title="variable">br</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a>.<br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bl"><span class="id" title="variable">bl</span></a> <a class="idref" href="mathcomp.algebra.interval.html#br"><span class="id" title="variable">br</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#le_boundl"><span class="id" title="definition">le_boundl</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bl"><span class="id" title="variable">bl</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BClose"><span class="id" title="abbreviation">BClose</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&amp;&amp;</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#le_boundr"><span class="id" title="definition">le_boundr</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BClose"><span class="id" title="abbreviation">BClose</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a>) <a class="idref" href="mathcomp.algebra.interval.html#br"><span class="id" title="variable">br</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a>.<br/>
  
 <br/>
-<span class="id" title="keyword">Lemma</span> <a name="le_boundr_refl"><span class="id" title="lemma">le_boundr_refl</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#reflexive"><span class="id" title="definition">reflexive</span></a> <a class="idref" href="mathcomp.algebra.interval.html#le_boundr"><span class="id" title="definition">le_boundr</span></a>.<br/>
+<span class="id" title="keyword">Lemma</span> <a name="le_boundl_refl"><span class="id" title="lemma">le_boundl_refl</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#reflexive"><span class="id" title="definition">reflexive</span></a> <a class="idref" href="mathcomp.algebra.interval.html#le_boundl"><span class="id" title="definition">le_boundl</span></a>.<br/>
  
 <br/>
-<span class="id" title="keyword">Hint Resolve</span> <span class="id" title="var">le_boundr_refl</span>.<br/>
+<span class="id" title="keyword">Hint Resolve</span> <span class="id" title="var">le_boundl_refl</span> : <span class="id" title="var">core</span>.<br/>
 
 <br/>
-<span class="id" title="keyword">Lemma</span> <a name="le_boundl_refl"><span class="id" title="lemma">le_boundl_refl</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#reflexive"><span class="id" title="definition">reflexive</span></a> <a class="idref" href="mathcomp.algebra.interval.html#le_boundl"><span class="id" title="definition">le_boundl</span></a>.<br/>
+<span class="id" title="keyword">Lemma</span> <a name="le_boundr_refl"><span class="id" title="lemma">le_boundr_refl</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#reflexive"><span class="id" title="definition">reflexive</span></a> <a class="idref" href="mathcomp.algebra.interval.html#le_boundr"><span class="id" title="definition">le_boundr</span></a>.<br/>
  
 <br/>
-<span class="id" title="keyword">Hint Resolve</span> <span class="id" title="var">le_boundl_refl</span>.<br/>
+<span class="id" title="keyword">Hint Resolve</span> <span class="id" title="var">le_boundr_refl</span> : <span class="id" title="var">core</span>.<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="le_boundl_trans"><span class="id" title="lemma">le_boundl_trans</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#transitive"><span class="id" title="definition">transitive</span></a> <a class="idref" href="mathcomp.algebra.interval.html#le_boundl"><span class="id" title="definition">le_boundl</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="le_boundr_trans"><span class="id" title="lemma">le_boundr_trans</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#transitive"><span class="id" title="definition">transitive</span></a> <a class="idref" href="mathcomp.algebra.interval.html#le_boundr"><span class="id" title="definition">le_boundr</span></a>.<br/>
 
 <br/>
 <span class="id" title="keyword">Lemma</span> <a name="le_boundl_bb"><span class="id" title="lemma">le_boundl_bb</span></a> <span class="id" title="var">x</span> <span class="id" title="var">b1</span> <span class="id" title="var">b2</span> :<br/>
-&nbsp;&nbsp;<a class="idref" href="mathcomp.algebra.interval.html#le_boundl"><span class="id" title="definition">le_boundl</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a>) (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#3b17cb5f3a16fa64a62421f68786f750"><span class="id" title="notation">==&gt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/>
+&nbsp;&nbsp;<a class="idref" href="mathcomp.algebra.interval.html#le_boundl"><span class="id" title="definition">le_boundl</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a>) (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#a133e82bab56729f895f9b2b31e837cd"><span class="id" title="notation">==&gt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
  
 <br/>
 <span class="id" title="keyword">Lemma</span> <a name="le_boundr_bb"><span class="id" title="lemma">le_boundr_bb</span></a> <span class="id" title="var">x</span> <span class="id" title="var">b1</span> <span class="id" title="var">b2</span> :<br/>
-&nbsp;&nbsp;<a class="idref" href="mathcomp.algebra.interval.html#le_boundr"><span class="id" title="definition">le_boundr</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a>) (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#3b17cb5f3a16fa64a62421f68786f750"><span class="id" title="notation">==&gt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/>
+&nbsp;&nbsp;<a class="idref" href="mathcomp.algebra.interval.html#le_boundr"><span class="id" title="definition">le_boundr</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a>) (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#a133e82bab56729f895f9b2b31e837cd"><span class="id" title="notation">==&gt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="le_boundl_anti"><span class="id" title="lemma">le_boundl_anti</span></a> <span class="id" title="var">b1</span> <span class="id" title="var">b2</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#le_boundl"><span class="id" title="definition">le_boundl</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&amp;&amp;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#le_boundl"><span class="id" title="definition">le_boundl</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="le_boundr_anti"><span class="id" title="lemma">le_boundr_anti</span></a> <span class="id" title="var">b1</span> <span class="id" title="var">b2</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#le_boundr"><span class="id" title="definition">le_boundr</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&amp;&amp;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#le_boundr"><span class="id" title="definition">le_boundr</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
  
 <br/>
 <span class="id" title="keyword">Lemma</span> <a name="itv_xx"><span class="id" title="lemma">itv_xx</span></a> <span class="id" title="var">x</span> <span class="id" title="var">bl</span> <span class="id" title="var">br</span> :<br/>
-&nbsp;&nbsp;<a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bl"><span class="id" title="variable">bl</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a>) (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#br"><span class="id" title="variable">br</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#20bf07099d6d8cf369383b22fd37862e"><span class="id" title="notation">=</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#20bf07099d6d8cf369383b22fd37862e"><span class="id" title="notation">i</span></a> <br/>
-&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">if</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#4b80c70cdb231351c5e129ba61f7f956"><span class="id" title="notation">~~</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#4b80c70cdb231351c5e129ba61f7f956"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#bl"><span class="id" title="variable">bl</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#14a7a9c7dc61f86bfb664d400fabaf8a"><span class="id" title="notation">||</span></a> <a class="idref" href="mathcomp.algebra.interval.html#br"><span class="id" title="variable">br</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#4b80c70cdb231351c5e129ba61f7f956"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">then</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#pred1"><span class="id" title="definition">pred1</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">else</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#pred0"><span class="id" title="definition">pred0</span></a>.<br/>
-
+&nbsp;&nbsp;<a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bl"><span class="id" title="variable">bl</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a>) (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#br"><span class="id" title="variable">br</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#1e6a438ff685c38fcd9034a94f271777"><span class="id" title="notation">=</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#1e6a438ff685c38fcd9034a94f271777"><span class="id" title="notation">i</span></a> <br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">if</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b3ebd0deddd84fd60e149cb5ef719351"><span class="id" title="notation">~~</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b3ebd0deddd84fd60e149cb5ef719351"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#bl"><span class="id" title="variable">bl</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">||</span></a> <a class="idref" href="mathcomp.algebra.interval.html#br"><span class="id" title="variable">br</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b3ebd0deddd84fd60e149cb5ef719351"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">then</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#pred1"><span class="id" title="definition">pred1</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">else</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred0"><span class="id" title="definition">pred0</span></a>.<br/>
+ 
 <br/>
-<span class="id" title="keyword">Lemma</span> <a name="itv_gte"><span class="id" title="lemma">itv_gte</span></a> <span class="id" title="var">ba</span> <span class="id" title="var">xa</span> <span class="id" title="var">bb</span> <span class="id" title="var">xb</span> :  <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">if</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#4b80c70cdb231351c5e129ba61f7f956"><span class="id" title="notation">~~</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#4b80c70cdb231351c5e129ba61f7f956"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#ba"><span class="id" title="variable">ba</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#14a7a9c7dc61f86bfb664d400fabaf8a"><span class="id" title="notation">||</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bb"><span class="id" title="variable">bb</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#4b80c70cdb231351c5e129ba61f7f956"><span class="id" title="notation">)</span></a> <br/>
-&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#ba"><span class="id" title="variable">ba</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a>) (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bb"><span class="id" title="variable">bb</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#20bf07099d6d8cf369383b22fd37862e"><span class="id" title="notation">=</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#20bf07099d6d8cf369383b22fd37862e"><span class="id" title="notation">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#pred0"><span class="id" title="definition">pred0</span></a>.<br/>
+<span class="id" title="keyword">Lemma</span> <a name="itv_gte"><span class="id" title="lemma">itv_gte</span></a> <span class="id" title="var">ba</span> <span class="id" title="var">xa</span> <span class="id" title="var">bb</span> <span class="id" title="var">xb</span> :  <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b3ebd0deddd84fd60e149cb5ef719351"><span class="id" title="notation">~~</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b3ebd0deddd84fd60e149cb5ef719351"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#ba"><span class="id" title="variable">ba</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">||</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bb"><span class="id" title="variable">bb</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b3ebd0deddd84fd60e149cb5ef719351"><span class="id" title="notation">)</span></a> <br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#ba"><span class="id" title="variable">ba</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a>) (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bb"><span class="id" title="variable">bb</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#1e6a438ff685c38fcd9034a94f271777"><span class="id" title="notation">=</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#1e6a438ff685c38fcd9034a94f271777"><span class="id" title="notation">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred0"><span class="id" title="definition">pred0</span></a>.<br/>
 
 <br/>
 <span class="id" title="keyword">Lemma</span> <a name="boundl_in_itv"><span class="id" title="lemma">boundl_in_itv</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">ba</span> <span class="id" title="var">xa</span> <span class="id" title="var">b</span>,<br/>
-&nbsp;&nbsp;<a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#ba"><span class="id" title="variable">ba</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a>) <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <br/>
-&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#ba"><span class="id" title="variable">ba</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">then</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">else</span></a> <a class="idref" href="mathcomp.algebra.interval.html#le_boundr"><span class="id" title="definition">le_boundr</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BClose"><span class="id" title="abbreviation">BClose</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a>) <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a>.<br/>
+&nbsp;&nbsp;<a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#ba"><span class="id" title="variable">ba</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a>) <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#ba"><span class="id" title="variable">ba</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">then</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">else</span></a> <a class="idref" href="mathcomp.algebra.interval.html#le_boundr"><span class="id" title="definition">le_boundr</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BClose"><span class="id" title="abbreviation">BClose</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a>) <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a>.<br/>
  
 <br/>
 <span class="id" title="keyword">Lemma</span> <a name="boundr_in_itv"><span class="id" title="lemma">boundr_in_itv</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">bb</span> <span class="id" title="var">xb</span> <span class="id" title="var">a</span>,<br/>
-&nbsp;&nbsp;<a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bb"><span class="id" title="variable">bb</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a><br/>
-&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bb"><span class="id" title="variable">bb</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">then</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">else</span></a> <a class="idref" href="mathcomp.algebra.interval.html#le_boundl"><span class="id" title="definition">le_boundl</span></a> <a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BClose"><span class="id" title="abbreviation">BClose</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a>).<br/>
+&nbsp;&nbsp;<a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bb"><span class="id" title="variable">bb</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bb"><span class="id" title="variable">bb</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">then</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">else</span></a> <a class="idref" href="mathcomp.algebra.interval.html#le_boundl"><span class="id" title="definition">le_boundl</span></a> <a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BClose"><span class="id" title="abbreviation">BClose</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a>).<br/>
  
 <br/>
-<span class="id" title="keyword">Definition</span> <a name="bound_in_itv"><span class="id" title="definition">bound_in_itv</span></a> := <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#boundl_in_itv"><span class="id" title="lemma">boundl_in_itv</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.algebra.interval.html#boundr_in_itv"><span class="id" title="lemma">boundr_in_itv</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">)</span></a>.<br/>
+<span class="id" title="keyword">Definition</span> <a name="bound_in_itv"><span class="id" title="definition">bound_in_itv</span></a> := <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#boundl_in_itv"><span class="id" title="lemma">boundl_in_itv</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.algebra.interval.html#boundr_in_itv"><span class="id" title="lemma">boundr_in_itv</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">)</span></a>.<br/>
 
 <br/>
-<span class="id" title="keyword">Lemma</span> <a name="itvP"><span class="id" title="lemma">itvP</span></a> : <span class="id" title="keyword">∀</span> (<span class="id" title="var">x</span> : <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>) (<span class="id" title="var">i</span> : <a class="idref" href="mathcomp.algebra.interval.html#interval"><span class="id" title="inductive">interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>), <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#itv_rewrite"><span class="id" title="definition">itv_rewrite</span></a> <a class="idref" href="mathcomp.algebra.interval.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a>.<br/>
+<span class="id" title="keyword">Lemma</span> <a name="itvP"><span class="id" title="lemma">itvP</span></a> : <span class="id" title="keyword">∀</span> (<span class="id" title="var">x</span> : <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>) (<span class="id" title="var">i</span> : <a class="idref" href="mathcomp.algebra.interval.html#interval"><span class="id" title="inductive">interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>), <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#itv_rewrite"><span class="id" title="definition">itv_rewrite</span></a> <a class="idref" href="mathcomp.algebra.interval.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a>.<br/>
 
 <br/>
-<span class="id" title="keyword">Hint Rewrite</span> <a class="idref" href="mathcomp.algebra.ssrint.html#intP"><span class="id" title="lemma">intP</span></a>.<br/>
 
 <br/>
+<span class="id" title="keyword">Definition</span> <a name="itv_intersection"><span class="id" title="definition">itv_intersection</span></a> (<span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.algebra.interval.html#interval"><span class="id" title="inductive">interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>) : <a class="idref" href="mathcomp.algebra.interval.html#interval"><span class="id" title="inductive">interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a> :=<br/>
+&nbsp;&nbsp;<span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <span class="id" title="var">x</span> <span class="id" title="var">x'</span> := <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <span class="id" title="tactic">in</span><br/>
+&nbsp;&nbsp;<span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <span class="id" title="var">y</span> <span class="id" title="var">y'</span> := <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <span class="id" title="tactic">in</span><br/>
+&nbsp;&nbsp;<a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;(<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#le_boundl"><span class="id" title="definition">le_boundl</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">then</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">else</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a>)<br/>
+&nbsp;&nbsp;&nbsp;&nbsp;(<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#le_boundr"><span class="id" title="definition">le_boundr</span></a> <span class="id" title="var">x'</span> <span class="id" title="var">y'</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">then</span></a> <span class="id" title="var">x'</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">else</span></a> <span class="id" title="var">y'</span>).<br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="itv_intersection1i"><span class="id" title="definition">itv_intersection1i</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#left_id"><span class="id" title="definition">left_id</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2d0f4f3a8486d97a7c68fd4d2f96ccac"><span class="id" title="notation">`]-</span></a><a class="idref" href="mathcomp.algebra.interval.html#2d0f4f3a8486d97a7c68fd4d2f96ccac"><span class="id" title="notation">oo</span></a><a class="idref" href="mathcomp.algebra.interval.html#2d0f4f3a8486d97a7c68fd4d2f96ccac"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2d0f4f3a8486d97a7c68fd4d2f96ccac"><span class="id" title="notation">+</span></a><a class="idref" href="mathcomp.algebra.interval.html#2d0f4f3a8486d97a7c68fd4d2f96ccac"><span class="id" title="notation">oo</span></a><a class="idref" href="mathcomp.algebra.interval.html#2d0f4f3a8486d97a7c68fd4d2f96ccac"><span class="id" title="notation">[</span></a> <a class="idref" href="mathcomp.algebra.interval.html#itv_intersection"><span class="id" title="definition">itv_intersection</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="itv_intersectioni1"><span class="id" title="definition">itv_intersectioni1</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#right_id"><span class="id" title="definition">right_id</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2d0f4f3a8486d97a7c68fd4d2f96ccac"><span class="id" title="notation">`]-</span></a><a class="idref" href="mathcomp.algebra.interval.html#2d0f4f3a8486d97a7c68fd4d2f96ccac"><span class="id" title="notation">oo</span></a><a class="idref" href="mathcomp.algebra.interval.html#2d0f4f3a8486d97a7c68fd4d2f96ccac"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2d0f4f3a8486d97a7c68fd4d2f96ccac"><span class="id" title="notation">+</span></a><a class="idref" href="mathcomp.algebra.interval.html#2d0f4f3a8486d97a7c68fd4d2f96ccac"><span class="id" title="notation">oo</span></a><a class="idref" href="mathcomp.algebra.interval.html#2d0f4f3a8486d97a7c68fd4d2f96ccac"><span class="id" title="notation">[</span></a> <a class="idref" href="mathcomp.algebra.interval.html#itv_intersection"><span class="id" title="definition">itv_intersection</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="itv_intersectionii"><span class="id" title="lemma">itv_intersectionii</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#idempotent"><span class="id" title="definition">idempotent</span></a> <a class="idref" href="mathcomp.algebra.interval.html#itv_intersection"><span class="id" title="definition">itv_intersection</span></a>.<br/>
+ 
+<br/>
 <span class="id" title="keyword">Definition</span> <a name="subitv"><span class="id" title="definition">subitv</span></a> (<span class="id" title="var">i1</span> <span class="id" title="var">i2</span> : <a class="idref" href="mathcomp.algebra.interval.html#interval"><span class="id" title="inductive">interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>) :=<br/>
 &nbsp;&nbsp;<span class="id" title="keyword">match</span> <a class="idref" href="mathcomp.algebra.interval.html#i1"><span class="id" title="variable">i1</span></a>, <a class="idref" href="mathcomp.algebra.interval.html#i2"><span class="id" title="variable">i2</span></a> <span class="id" title="keyword">with</span><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;| <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <span class="id" title="var">a1</span> <span class="id" title="var">b1</span>, <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <span class="id" title="var">a2</span> <span class="id" title="var">b2</span> ⇒ <a class="idref" href="mathcomp.algebra.interval.html#le_boundl"><span class="id" title="definition">le_boundl</span></a> <span class="id" title="var">a2</span> <span class="id" title="var">a1</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&amp;&amp;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#le_boundr"><span class="id" title="definition">le_boundr</span></a> <span class="id" title="var">b1</span> <span class="id" title="var">b2</span><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;| <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <span class="id" title="var">a1</span> <span class="id" title="var">b1</span>, <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <span class="id" title="var">a2</span> <span class="id" title="var">b2</span> ⇒ <a class="idref" href="mathcomp.algebra.interval.html#le_boundl"><span class="id" title="definition">le_boundl</span></a> <span class="id" title="var">a2</span> <span class="id" title="var">a1</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&amp;&amp;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#le_boundr"><span class="id" title="definition">le_boundr</span></a> <span class="id" title="var">b1</span> <span class="id" title="var">b2</span><br/>
 &nbsp;&nbsp;<span class="id" title="keyword">end</span>.<br/>
 
 <br/>
-<span class="id" title="keyword">Lemma</span> <a name="subitvP"><span class="id" title="lemma">subitvP</span></a> : <span class="id" title="keyword">∀</span> (<span class="id" title="var">i2</span> <span class="id" title="var">i1</span> : <a class="idref" href="mathcomp.algebra.interval.html#interval"><span class="id" title="inductive">interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>), <br/>
-&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#subitv"><span class="id" title="definition">subitv</span></a> <a class="idref" href="mathcomp.algebra.interval.html#i1"><span class="id" title="variable">i1</span></a> <a class="idref" href="mathcomp.algebra.interval.html#i2"><span class="id" title="variable">i2</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.algebra.interval.html#i1"><span class="id" title="variable">i1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#i2"><span class="id" title="variable">i2</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">}</span></a>.<br/>
+<span class="id" title="keyword">Lemma</span> <a name="subitvP"><span class="id" title="lemma">subitvP</span></a> : <span class="id" title="keyword">∀</span> (<span class="id" title="var">i2</span> <span class="id" title="var">i1</span> : <a class="idref" href="mathcomp.algebra.interval.html#interval"><span class="id" title="inductive">interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>), <a class="idref" href="mathcomp.algebra.interval.html#subitv"><span class="id" title="definition">subitv</span></a> <a class="idref" href="mathcomp.algebra.interval.html#i1"><span class="id" title="variable">i1</span></a> <a class="idref" href="mathcomp.algebra.interval.html#i2"><span class="id" title="variable">i2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.algebra.interval.html#i1"><span class="id" title="variable">i1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#i2"><span class="id" title="variable">i2</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">}</span></a>.<br/>
 
 <br/>
-<span class="id" title="keyword">Lemma</span> <a name="subitvPr"><span class="id" title="lemma">subitvPr</span></a> : <span class="id" title="keyword">∀</span> (<span class="id" title="var">a</span> <span class="id" title="var">b1</span> <span class="id" title="var">b2</span> : <a class="idref" href="mathcomp.algebra.interval.html#itv_bound"><span class="id" title="inductive">itv_bound</span></a> <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>),<br/>
-&nbsp;&nbsp;<a class="idref" href="mathcomp.algebra.interval.html#le_boundr"><span class="id" title="definition">le_boundr</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">subset</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">≤</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">)}</span></a>.<br/>
+<span class="id" title="keyword">Lemma</span> <a name="subitvPr"><span class="id" title="lemma">subitvPr</span></a> (<span class="id" title="var">a</span> <span class="id" title="var">b1</span> <span class="id" title="var">b2</span> : <a class="idref" href="mathcomp.algebra.interval.html#itv_bound"><span class="id" title="inductive">itv_bound</span></a> <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>) :<br/>
+&nbsp;&nbsp;<a class="idref" href="mathcomp.algebra.interval.html#le_boundr"><span class="id" title="definition">le_boundr</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">subset</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b1"><span class="id" title="variable">b1</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">≤</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b2"><span class="id" title="variable">b2</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">)}</span></a>.<br/>
  
 <br/>
-<span class="id" title="keyword">Lemma</span> <a name="subitvPl"><span class="id" title="lemma">subitvPl</span></a> : <span class="id" title="keyword">∀</span> (<span class="id" title="var">a1</span> <span class="id" title="var">a2</span> <span class="id" title="var">b</span> : <a class="idref" href="mathcomp.algebra.interval.html#itv_bound"><span class="id" title="inductive">itv_bound</span></a> <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>),<br/>
-&nbsp;&nbsp;<a class="idref" href="mathcomp.algebra.interval.html#le_boundl"><span class="id" title="definition">le_boundl</span></a> <a class="idref" href="mathcomp.algebra.interval.html#a2"><span class="id" title="variable">a2</span></a> <a class="idref" href="mathcomp.algebra.interval.html#a1"><span class="id" title="variable">a1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">subset</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#a1"><span class="id" title="variable">a1</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">≤</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#a2"><span class="id" title="variable">a2</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#53295d8f18390300c5a24f66e0bcda98"><span class="id" title="notation">)}</span></a>.<br/>
+<span class="id" title="keyword">Lemma</span> <a name="subitvPl"><span class="id" title="lemma">subitvPl</span></a> (<span class="id" title="var">a1</span> <span class="id" title="var">a2</span> <span class="id" title="var">b</span> : <a class="idref" href="mathcomp.algebra.interval.html#itv_bound"><span class="id" title="inductive">itv_bound</span></a> <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>) :<br/>
+&nbsp;&nbsp;<a class="idref" href="mathcomp.algebra.interval.html#le_boundl"><span class="id" title="definition">le_boundl</span></a> <a class="idref" href="mathcomp.algebra.interval.html#a2"><span class="id" title="variable">a2</span></a> <a class="idref" href="mathcomp.algebra.interval.html#a1"><span class="id" title="variable">a1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">subset</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#a1"><span class="id" title="variable">a1</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">≤</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#a2"><span class="id" title="variable">a2</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">)}</span></a>.<br/>
  
 <br/>
-<span class="id" title="keyword">Lemma</span> <a name="lersif_in_itv"><span class="id" title="lemma">lersif_in_itv</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">ba</span> <span class="id" title="var">bb</span> <span class="id" title="var">xa</span> <span class="id" title="var">xb</span> <span class="id" title="var">x</span>,<br/>
-&nbsp;&nbsp;<a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#ba"><span class="id" title="variable">ba</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a>) (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bb"><span class="id" title="variable">bb</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#ba"><span class="id" title="variable">ba</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#14a7a9c7dc61f86bfb664d400fabaf8a"><span class="id" title="notation">||</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bb"><span class="id" title="variable">bb</span></a>.<br/>
-
-<br/>
-<span class="id" title="keyword">Lemma</span> <a name="ltr_in_itv"><span class="id" title="lemma">ltr_in_itv</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">ba</span> <span class="id" title="var">bb</span> <span class="id" title="var">xa</span> <span class="id" title="var">xb</span> <span class="id" title="var">x</span>, <a class="idref" href="mathcomp.algebra.interval.html#ba"><span class="id" title="variable">ba</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#14a7a9c7dc61f86bfb664d400fabaf8a"><span class="id" title="notation">||</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bb"><span class="id" title="variable">bb</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
-&nbsp;&nbsp;<a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#ba"><span class="id" title="variable">ba</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a>) (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bb"><span class="id" title="variable">bb</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#388c172bf8d34ef0bf11898cd56f8d7b"><span class="id" title="notation">&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a>.<br/>
-
+<span class="id" title="keyword">Lemma</span> <a name="lersif_in_itv"><span class="id" title="lemma">lersif_in_itv</span></a> <span class="id" title="var">ba</span> <span class="id" title="var">bb</span> <span class="id" title="var">xa</span> <span class="id" title="var">xb</span> <span class="id" title="var">x</span> :<br/>
+&nbsp;&nbsp;<a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#ba"><span class="id" title="variable">ba</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a>) (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bb"><span class="id" title="variable">bb</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#ba"><span class="id" title="variable">ba</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">||</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bb"><span class="id" title="variable">bb</span></a>.<br/>
+ 
 <br/>
-<span class="id" title="keyword">Lemma</span> <a name="ler_in_itv"><span class="id" title="lemma">ler_in_itv</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">ba</span> <span class="id" title="var">bb</span> <span class="id" title="var">xa</span> <span class="id" title="var">xb</span> <span class="id" title="var">x</span>,<br/>
-&nbsp;&nbsp;<a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#ba"><span class="id" title="variable">ba</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a>) (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bb"><span class="id" title="variable">bb</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#1065783963a393d1eafa2137291f2495"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a>.<br/>
+<span class="id" title="keyword">Lemma</span> <a name="ltr_in_itv"><span class="id" title="lemma">ltr_in_itv</span></a> <span class="id" title="var">ba</span> <span class="id" title="var">bb</span> <span class="id" title="var">xa</span> <span class="id" title="var">xb</span> <span class="id" title="var">x</span> :<br/>
+&nbsp;&nbsp;<a class="idref" href="mathcomp.algebra.interval.html#ba"><span class="id" title="variable">ba</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">||</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bb"><span class="id" title="variable">bb</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#ba"><span class="id" title="variable">ba</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a>) (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bb"><span class="id" title="variable">bb</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation">&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a>.<br/>
  
 <br/>
-<span class="id" title="keyword">Lemma</span> <a name="mem0_itvcc_xNx"><span class="id" title="lemma">mem0_itvcc_xNx</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span>, <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a>0 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">`[</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#941c6d086004545bd62614d0213e75e5"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a>0 <a class="idref" href="mathcomp.algebra.ssrnum.html#1065783963a393d1eafa2137291f2495"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/>
-
+<span class="id" title="keyword">Lemma</span> <a name="ler_in_itv"><span class="id" title="lemma">ler_in_itv</span></a> <span class="id" title="var">ba</span> <span class="id" title="var">bb</span> <span class="id" title="var">xa</span> <span class="id" title="var">xb</span> <span class="id" title="var">x</span> :<br/>
+&nbsp;&nbsp;<a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#ba"><span class="id" title="variable">ba</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a>) (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bb"><span class="id" title="variable">bb</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#cb42ec59ad57b25928e1718b4e69e031"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a>.<br/>
+ 
 <br/>
-<span class="id" title="keyword">Lemma</span> <a name="mem0_itvoo_xNx"><span class="id" title="lemma">mem0_itvoo_xNx</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span>, 0 <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#5d6177042cf2728bb3a48ad4d7fef36d"><span class="id" title="notation">`](</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#941c6d086004545bd62614d0213e75e5"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.algebra.interval.html#5d6177042cf2728bb3a48ad4d7fef36d"><span class="id" title="notation">),</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.algebra.interval.html#5d6177042cf2728bb3a48ad4d7fef36d"><span class="id" title="notation">[</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a>0 <a class="idref" href="mathcomp.algebra.ssrnum.html#388c172bf8d34ef0bf11898cd56f8d7b"><span class="id" title="notation">&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/>
-
+<span class="id" title="keyword">Lemma</span> <a name="mem0_itvcc_xNx"><span class="id" title="lemma">mem0_itvcc_xNx</span></a> <span class="id" title="var">x</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a>0 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">`[</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a>0 <a class="idref" href="mathcomp.algebra.ssrnum.html#cb42ec59ad57b25928e1718b4e69e031"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
+ 
 <br/>
-<span class="id" title="keyword">Lemma</span> <a name="itv_splitI"><span class="id" title="lemma">itv_splitI</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">a</span> <span class="id" title="var">b</span>, <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span>,<br/>
-&nbsp;&nbsp;<a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> <span class="id" title="var">_</span>)<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">&amp;&amp;</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> <span class="id" title="var">_</span>) <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#49ac24efa716d8b0ee8943bc1d1769a9"><span class="id" title="notation">)</span></a>.<br/>
+<span class="id" title="keyword">Lemma</span> <a name="mem0_itvoo_xNx"><span class="id" title="lemma">mem0_itvoo_xNx</span></a> <span class="id" title="var">x</span> : 0 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#ebff9f8c4fe58806999ff1c12ccee445"><span class="id" title="notation">`](</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.algebra.interval.html#ebff9f8c4fe58806999ff1c12ccee445"><span class="id" title="notation">),</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.algebra.interval.html#ebff9f8c4fe58806999ff1c12ccee445"><span class="id" title="notation">[</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a>0 <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation">&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
  
 <br/>
-<span class="id" title="keyword">Lemma</span> <a name="real_lersifN"><span class="id" title="lemma">real_lersifN</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <span class="id" title="var">b</span> : <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#Num.real"><span class="id" title="abbreviation">Num.real</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#Num.real"><span class="id" title="abbreviation">Num.real</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
-&nbsp;&nbsp;<a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">if</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#4b80c70cdb231351c5e129ba61f7f956"><span class="id" title="notation">~~</span></a><a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#4b80c70cdb231351c5e129ba61f7f956"><span class="id" title="notation">~~</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#4b80c70cdb231351c5e129ba61f7f956"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1c796095ee2c250ae9d97f3c7d8c93ac"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#4b80c70cdb231351c5e129ba61f7f956"><span class="id" title="notation">)</span></a>.<br/>
+<span class="id" title="keyword">Lemma</span> <a name="itv_splitI"><span class="id" title="lemma">itv_splitI</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">a</span> <span class="id" title="var">b</span> <span class="id" title="var">x</span>,<br/>
+&nbsp;&nbsp;<a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> <span class="id" title="var">_</span>)<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&amp;&amp;</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> <span class="id" title="var">_</span>) <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a>.<br/>
  
 <br/>
 <span class="id" title="keyword">Lemma</span> <a name="oppr_itv"><span class="id" title="lemma">oppr_itv</span></a> <span class="id" title="var">ba</span> <span class="id" title="var">bb</span> (<span class="id" title="var">xa</span> <span class="id" title="var">xb</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>) :<br/>
-&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#941c6d086004545bd62614d0213e75e5"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#ba"><span class="id" title="variable">ba</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a>) (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bb"><span class="id" title="variable">bb</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <br/>
-&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bb"><span class="id" title="variable">bb</span></a> (<a class="idref" href="mathcomp.algebra.ssralg.html#941c6d086004545bd62614d0213e75e5"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a>)) (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#ba"><span class="id" title="variable">ba</span></a> (<a class="idref" href="mathcomp.algebra.ssralg.html#941c6d086004545bd62614d0213e75e5"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a>))<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#ba"><span class="id" title="variable">ba</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a>) (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bb"><span class="id" title="variable">bb</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bb"><span class="id" title="variable">bb</span></a> (<a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a>)) (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#ba"><span class="id" title="variable">ba</span></a> (<a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a>))<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
  
 <br/>
-<span class="id" title="keyword">Lemma</span> <a name="oppr_itvoo"><span class="id" title="lemma">oppr_itvoo</span></a> (<span class="id" title="var">a</span> <span class="id" title="var">b</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>) : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#941c6d086004545bd62614d0213e75e5"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#5d6177042cf2728bb3a48ad4d7fef36d"><span class="id" title="notation">`]</span></a><a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.algebra.interval.html#5d6177042cf2728bb3a48ad4d7fef36d"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="mathcomp.algebra.interval.html#5d6177042cf2728bb3a48ad4d7fef36d"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#5d6177042cf2728bb3a48ad4d7fef36d"><span class="id" title="notation">`](</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#941c6d086004545bd62614d0213e75e5"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="mathcomp.algebra.interval.html#5d6177042cf2728bb3a48ad4d7fef36d"><span class="id" title="notation">),</span></a> <a class="idref" href="mathcomp.algebra.interval.html#5d6177042cf2728bb3a48ad4d7fef36d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#941c6d086004545bd62614d0213e75e5"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.algebra.interval.html#5d6177042cf2728bb3a48ad4d7fef36d"><span class="id" title="notation">)[</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/>
+<span class="id" title="keyword">Lemma</span> <a name="oppr_itvoo"><span class="id" title="lemma">oppr_itvoo</span></a> (<span class="id" title="var">a</span> <span class="id" title="var">b</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>) : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#ebff9f8c4fe58806999ff1c12ccee445"><span class="id" title="notation">`]</span></a><a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.algebra.interval.html#ebff9f8c4fe58806999ff1c12ccee445"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="mathcomp.algebra.interval.html#ebff9f8c4fe58806999ff1c12ccee445"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#ebff9f8c4fe58806999ff1c12ccee445"><span class="id" title="notation">`](</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="mathcomp.algebra.interval.html#ebff9f8c4fe58806999ff1c12ccee445"><span class="id" title="notation">),</span></a> <a class="idref" href="mathcomp.algebra.interval.html#ebff9f8c4fe58806999ff1c12ccee445"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.algebra.interval.html#ebff9f8c4fe58806999ff1c12ccee445"><span class="id" title="notation">)[</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
  
 <br/>
-<span class="id" title="keyword">Lemma</span> <a name="oppr_itvco"><span class="id" title="lemma">oppr_itvco</span></a> (<span class="id" title="var">a</span> <span class="id" title="var">b</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>) : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#941c6d086004545bd62614d0213e75e5"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#e13694bd4c96b2ebd74cba5937d97bac"><span class="id" title="notation">`[</span></a><a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.algebra.interval.html#e13694bd4c96b2ebd74cba5937d97bac"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="mathcomp.algebra.interval.html#e13694bd4c96b2ebd74cba5937d97bac"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#9776a398e1a32aa2aa525fec3dcf7a09"><span class="id" title="notation">`](</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#941c6d086004545bd62614d0213e75e5"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="mathcomp.algebra.interval.html#9776a398e1a32aa2aa525fec3dcf7a09"><span class="id" title="notation">),</span></a> <a class="idref" href="mathcomp.algebra.interval.html#9776a398e1a32aa2aa525fec3dcf7a09"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#941c6d086004545bd62614d0213e75e5"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.algebra.interval.html#9776a398e1a32aa2aa525fec3dcf7a09"><span class="id" title="notation">)]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/>
+<span class="id" title="keyword">Lemma</span> <a name="oppr_itvco"><span class="id" title="lemma">oppr_itvco</span></a> (<span class="id" title="var">a</span> <span class="id" title="var">b</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>) : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#957313378acc4cb77b1d2f647eca85b3"><span class="id" title="notation">`[</span></a><a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.algebra.interval.html#957313378acc4cb77b1d2f647eca85b3"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="mathcomp.algebra.interval.html#957313378acc4cb77b1d2f647eca85b3"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#9ad860ccdfe75680d287151e25f339b9"><span class="id" title="notation">`](</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="mathcomp.algebra.interval.html#9ad860ccdfe75680d287151e25f339b9"><span class="id" title="notation">),</span></a> <a class="idref" href="mathcomp.algebra.interval.html#9ad860ccdfe75680d287151e25f339b9"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.algebra.interval.html#9ad860ccdfe75680d287151e25f339b9"><span class="id" title="notation">)]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
  
 <br/>
-<span class="id" title="keyword">Lemma</span> <a name="oppr_itvoc"><span class="id" title="lemma">oppr_itvoc</span></a> (<span class="id" title="var">a</span> <span class="id" title="var">b</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>) : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#941c6d086004545bd62614d0213e75e5"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#9776a398e1a32aa2aa525fec3dcf7a09"><span class="id" title="notation">`]</span></a><a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.algebra.interval.html#9776a398e1a32aa2aa525fec3dcf7a09"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="mathcomp.algebra.interval.html#9776a398e1a32aa2aa525fec3dcf7a09"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#e13694bd4c96b2ebd74cba5937d97bac"><span class="id" title="notation">`[(</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#941c6d086004545bd62614d0213e75e5"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="mathcomp.algebra.interval.html#e13694bd4c96b2ebd74cba5937d97bac"><span class="id" title="notation">),</span></a> <a class="idref" href="mathcomp.algebra.interval.html#e13694bd4c96b2ebd74cba5937d97bac"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#941c6d086004545bd62614d0213e75e5"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.algebra.interval.html#e13694bd4c96b2ebd74cba5937d97bac"><span class="id" title="notation">)[</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/>
+<span class="id" title="keyword">Lemma</span> <a name="oppr_itvoc"><span class="id" title="lemma">oppr_itvoc</span></a> (<span class="id" title="var">a</span> <span class="id" title="var">b</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>) : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#9ad860ccdfe75680d287151e25f339b9"><span class="id" title="notation">`]</span></a><a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.algebra.interval.html#9ad860ccdfe75680d287151e25f339b9"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="mathcomp.algebra.interval.html#9ad860ccdfe75680d287151e25f339b9"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#957313378acc4cb77b1d2f647eca85b3"><span class="id" title="notation">`[(</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="mathcomp.algebra.interval.html#957313378acc4cb77b1d2f647eca85b3"><span class="id" title="notation">),</span></a> <a class="idref" href="mathcomp.algebra.interval.html#957313378acc4cb77b1d2f647eca85b3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.algebra.interval.html#957313378acc4cb77b1d2f647eca85b3"><span class="id" title="notation">)[</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
  
 <br/>
-<span class="id" title="keyword">Lemma</span> <a name="oppr_itvcc"><span class="id" title="lemma">oppr_itvcc</span></a> (<span class="id" title="var">a</span> <span class="id" title="var">b</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>) : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#941c6d086004545bd62614d0213e75e5"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">`[</span></a><a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">`[(</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#941c6d086004545bd62614d0213e75e5"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">),</span></a> <a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#941c6d086004545bd62614d0213e75e5"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.algebra.interval.html#0d2438566c38b95c9bc6204c40c6c9af"><span class="id" title="notation">)]</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/>
+<span class="id" title="keyword">Lemma</span> <a name="oppr_itvcc"><span class="id" title="lemma">oppr_itvcc</span></a> (<span class="id" title="var">a</span> <span class="id" title="var">b</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo.R"><span class="id" title="variable">R</span></a>) : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">`[</span></a><a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">`[(</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">),</span></a> <a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.ssralg.html#8d0566c961139ec21811f52ef0c317db"><span class="id" title="notation">-</span></a><a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">)]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/>
  
 <br/>
 <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.interval.html#IntervalPo"><span class="id" title="section">IntervalPo</span></a>.<br/>
 
 <br/>
-<span class="id" title="keyword">Notation</span> <a name="BOpen"><span class="id" title="abbreviation">BOpen</span></a> := (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a>).<br/>
-<span class="id" title="keyword">Notation</span> <a name="BClose"><span class="id" title="abbreviation">BClose</span></a> := (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a>).<br/>
-<span class="id" title="keyword">Notation</span> <a name="1b23dabf87b87c155f5c39a03cf252fd"><span class="id" title="notation">&quot;</span></a>`[ a , b ]" := (<a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BClose"><span class="id" title="abbreviation">BClose</span></a> <span class="id" title="var">a</span>) (<a class="idref" href="mathcomp.algebra.interval.html#BClose"><span class="id" title="abbreviation">BClose</span></a> <span class="id" title="var">b</span>))<br/>
-&nbsp;&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">a</span>, <span class="id" title="var">b</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 9 , <span class="id" title="var">format</span> "`[ a ,  b ]") : <span class="id" title="var">ring_scope</span>.<br/>
-<span class="id" title="keyword">Notation</span> <a name="cbbc44194330d5df3c5926da24c44c66"><span class="id" title="notation">&quot;</span></a>`] a , b ]" := (<a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen"><span class="id" title="abbreviation">BOpen</span></a> <span class="id" title="var">a</span>) (<a class="idref" href="mathcomp.algebra.interval.html#BClose"><span class="id" title="abbreviation">BClose</span></a> <span class="id" title="var">b</span>))<br/>
-&nbsp;&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">a</span>, <span class="id" title="var">b</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 9 , <span class="id" title="var">format</span> "`] a ,  b ]") : <span class="id" title="var">ring_scope</span>.<br/>
-<span class="id" title="keyword">Notation</span> <a name="7f598a2ea63782d9411311b8a5b31ec4"><span class="id" title="notation">&quot;</span></a>`[ a , b [" := (<a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BClose"><span class="id" title="abbreviation">BClose</span></a> <span class="id" title="var">a</span>) (<a class="idref" href="mathcomp.algebra.interval.html#BOpen"><span class="id" title="abbreviation">BOpen</span></a> <span class="id" title="var">b</span>))<br/>
-&nbsp;&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">a</span>, <span class="id" title="var">b</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 9 , <span class="id" title="var">format</span> "`[ a ,  b [") : <span class="id" title="var">ring_scope</span>.<br/>
-<span class="id" title="keyword">Notation</span> <a name="2e8617f61b689dc49fc99a5898babaf3"><span class="id" title="notation">&quot;</span></a>`] a , b [" := (<a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen"><span class="id" title="abbreviation">BOpen</span></a> <span class="id" title="var">a</span>) (<a class="idref" href="mathcomp.algebra.interval.html#BOpen"><span class="id" title="abbreviation">BOpen</span></a> <span class="id" title="var">b</span>))<br/>
-&nbsp;&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">a</span>, <span class="id" title="var">b</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 9 , <span class="id" title="var">format</span> "`] a ,  b [") : <span class="id" title="var">ring_scope</span>.<br/>
-<span class="id" title="keyword">Notation</span> <a name="f98d6dca6f228c955e58f5882c1f46dd"><span class="id" title="notation">&quot;</span></a>`] '-oo' , b ]" := (<a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> <span class="id" title="var">_</span>) (<a class="idref" href="mathcomp.algebra.interval.html#BClose"><span class="id" title="abbreviation">BClose</span></a> <span class="id" title="var">b</span>))<br/>
-&nbsp;&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">b</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 9 , <span class="id" title="var">format</span> "`] '-oo' ,  b ]") : <span class="id" title="var">ring_scope</span>.<br/>
-<span class="id" title="keyword">Notation</span> <a name="b76159d3095994358e02438cbda0e8dc"><span class="id" title="notation">&quot;</span></a>`] '-oo' , b [" := (<a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> <span class="id" title="var">_</span>) (<a class="idref" href="mathcomp.algebra.interval.html#BOpen"><span class="id" title="abbreviation">BOpen</span></a> <span class="id" title="var">b</span>))<br/>
-&nbsp;&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">b</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 9 , <span class="id" title="var">format</span> "`] '-oo' ,  b [") : <span class="id" title="var">ring_scope</span>.<br/>
-<span class="id" title="keyword">Notation</span> <a name="5c418f5a1d748d89694d4fdc12d0e150"><span class="id" title="notation">&quot;</span></a>`[ a , '+oo' [" := (<a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BClose"><span class="id" title="abbreviation">BClose</span></a> <span class="id" title="var">a</span>) (<a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> <span class="id" title="var">_</span>))<br/>
-&nbsp;&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">a</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 9 , <span class="id" title="var">format</span> "`[ a ,  '+oo' [") : <span class="id" title="var">ring_scope</span>.<br/>
-<span class="id" title="keyword">Notation</span> <a name="e96e2d5a7b2075039ce29a159daa96fc"><span class="id" title="notation">&quot;</span></a>`] a , '+oo' [" := (<a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen"><span class="id" title="abbreviation">BOpen</span></a> <span class="id" title="var">a</span>) (<a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> <span class="id" title="var">_</span>))<br/>
-&nbsp;&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">a</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 9 , <span class="id" title="var">format</span> "`] a ,  '+oo' [") : <span class="id" title="var">ring_scope</span>.<br/>
-<span class="id" title="keyword">Notation</span> <a name="3495087d2de1936e210dc1e87cddee5f"><span class="id" title="notation">&quot;</span></a>`] -oo , '+oo' [" := (<a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> <span class="id" title="var">_</span>) (<a class="idref" href="mathcomp.algebra.interval.html#BInfty"><span class="id" title="constructor">BInfty</span></a> <span class="id" title="var">_</span>))<br/>
-&nbsp;&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "`] -oo ,  '+oo' [") : <span class="id" title="var">ring_scope</span>.<br/>
+<span class="id" title="keyword">Section</span> <a name="IntervalOrdered"><span class="id" title="section">IntervalOrdered</span></a>.<br/>
 
 <br/>
-<span class="id" title="keyword">Notation</span> <a name="bec03331256891011ac5a0ab95580e68"><span class="id" title="notation">&quot;</span></a>x &lt;= y ?&lt; 'if' b" := (<a class="idref" href="mathcomp.algebra.interval.html#lersif"><span class="id" title="definition">lersif</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <span class="id" title="var">b</span>)<br/>
-&nbsp;&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 70, <span class="id" title="var">y</span> <span class="id" title="tactic">at</span> <span class="id" title="var">next</span> <span class="id" title="keyword">level</span>,<br/>
-&nbsp;&nbsp;<span class="id" title="var">format</span> "x '[hv'  &lt;=  y '/'  ?&lt;  'if'  b ']'") : <span class="id" title="var">ring_scope</span>.<br/>
+<span class="id" title="keyword">Variable</span> <a name="IntervalOrdered.R"><span class="id" title="variable">R</span></a> : <a class="idref" href="mathcomp.algebra.ssrnum.html#Num.RealDomain.Exports.realDomainType"><span class="id" title="abbreviation">realDomainType</span></a>.<br/>
 
 <br/>
-<span class="id" title="keyword">Section</span> <a name="IntervalOrdered"><span class="id" title="section">IntervalOrdered</span></a>.<br/>
+<span class="id" title="keyword">Lemma</span> <a name="le_boundl_total"><span class="id" title="lemma">le_boundl_total</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#total"><span class="id" title="definition">total</span></a> (@<a class="idref" href="mathcomp.algebra.interval.html#le_boundl"><span class="id" title="definition">le_boundl</span></a> <a class="idref" href="mathcomp.algebra.interval.html#IntervalOrdered.R"><span class="id" title="variable">R</span></a>).<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="le_boundr_total"><span class="id" title="lemma">le_boundr_total</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#total"><span class="id" title="definition">total</span></a> (@<a class="idref" href="mathcomp.algebra.interval.html#le_boundr"><span class="id" title="definition">le_boundr</span></a> <a class="idref" href="mathcomp.algebra.interval.html#IntervalOrdered.R"><span class="id" title="variable">R</span></a>).<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="itv_splitU"><span class="id" title="lemma">itv_splitU</span></a> (<span class="id" title="var">xc</span> : <a class="idref" href="mathcomp.algebra.interval.html#IntervalOrdered.R"><span class="id" title="variable">R</span></a>) <span class="id" title="var">bc</span> <span class="id" title="var">a</span> <span class="id" title="var">b</span> : <a class="idref" href="mathcomp.algebra.interval.html#xc"><span class="id" title="variable">xc</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;<span class="id" title="keyword">∀</span> <span class="id" title="var">y</span>, <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b3ebd0deddd84fd60e149cb5ef719351"><span class="id" title="notation">~~</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bc"><span class="id" title="variable">bc</span></a>) <a class="idref" href="mathcomp.algebra.interval.html#xc"><span class="id" title="variable">xc</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">||</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bc"><span class="id" title="variable">bc</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xc"><span class="id" title="variable">xc</span></a>) <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a>.<br/>
 
 <br/>
-<span class="id" title="keyword">Variable</span> <a name="IntervalOrdered.R"><span class="id" title="variable">R</span></a> : <a class="idref" href="mathcomp.algebra.ssrnum.html#Num.RealDomain.Exports.realDomainType"><span class="id" title="abbreviation">realDomainType</span></a>.<br/>
+<span class="id" title="keyword">Lemma</span> <a name="itv_splitU2"><span class="id" title="lemma">itv_splitU2</span></a> (<span class="id" title="var">x</span> : <a class="idref" href="mathcomp.algebra.interval.html#IntervalOrdered.R"><span class="id" title="variable">R</span></a>) <span class="id" title="var">a</span> <span class="id" title="var">b</span> : <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/>
+&nbsp;&nbsp;<span class="id" title="keyword">∀</span> <span class="id" title="var">y</span>, <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#6e3f5b731a46299b833a2834f381d536"><span class="id" title="notation">[||</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#6e3f5b731a46299b833a2834f381d536"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen"><span class="id" title="abbreviation">BOpen</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#6e3f5b731a46299b833a2834f381d536"><span class="id" title="notation">),</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#6e3f5b731a46299b833a2834f381d536"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#6e3f5b731a46299b833a2834f381d536"><span class="id" title="notation">)</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#6e3f5b731a46299b833a2834f381d536"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#6e3f5b731a46299b833a2834f381d536"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen"><span class="id" title="abbreviation">BOpen</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a>) <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#6e3f5b731a46299b833a2834f381d536"><span class="id" title="notation">)]</span></a>.<br/>
 
 <br/>
-<span class="id" title="keyword">Lemma</span> <a name="lersifN"><span class="id" title="lemma">lersifN</span></a> (<span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.algebra.interval.html#IntervalOrdered.R"><span class="id" title="variable">R</span></a>) <span class="id" title="var">b</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bec03331256891011ac5a0ab95580e68"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bec03331256891011ac5a0ab95580e68"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bec03331256891011ac5a0ab95580e68"><span class="id" title="notation">if</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#4b80c70cdb231351c5e129ba61f7f956"><span class="id" title="notation">~~</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#4b80c70cdb231351c5e129ba61f7f956"><span class="id" title="notation">~~</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#4b80c70cdb231351c5e129ba61f7f956"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bec03331256891011ac5a0ab95580e68"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bec03331256891011ac5a0ab95580e68"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bec03331256891011ac5a0ab95580e68"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#4b80c70cdb231351c5e129ba61f7f956"><span class="id" title="notation">)</span></a>.<br/>
- 
+<span class="id" title="keyword">Lemma</span> <a name="itv_intersectionC"><span class="id" title="lemma">itv_intersectionC</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#commutative"><span class="id" title="definition">commutative</span></a> (@<a class="idref" href="mathcomp.algebra.interval.html#itv_intersection"><span class="id" title="definition">itv_intersection</span></a> <a class="idref" href="mathcomp.algebra.interval.html#IntervalOrdered.R"><span class="id" title="variable">R</span></a>).<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="itv_intersectionA"><span class="id" title="lemma">itv_intersectionA</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#associative"><span class="id" title="definition">associative</span></a> (@<a class="idref" href="mathcomp.algebra.interval.html#itv_intersection"><span class="id" title="definition">itv_intersection</span></a> <a class="idref" href="mathcomp.algebra.interval.html#IntervalOrdered.R"><span class="id" title="variable">R</span></a>).<br/>
+
 <br/>
-<span class="id" title="keyword">Lemma</span> <a name="itv_splitU"><span class="id" title="lemma">itv_splitU</span></a> (<span class="id" title="var">xc</span> : <a class="idref" href="mathcomp.algebra.interval.html#IntervalOrdered.R"><span class="id" title="variable">R</span></a>) <span class="id" title="var">bc</span> <span class="id" title="var">a</span> <span class="id" title="var">b</span> : <a class="idref" href="mathcomp.algebra.interval.html#xc"><span class="id" title="variable">xc</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
-&nbsp;&nbsp;<span class="id" title="keyword">∀</span> <span class="id" title="var">y</span>, <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#14a7a9c7dc61f86bfb664d400fabaf8a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#4b80c70cdb231351c5e129ba61f7f956"><span class="id" title="notation">~~</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bc"><span class="id" title="variable">bc</span></a>) <a class="idref" href="mathcomp.algebra.interval.html#xc"><span class="id" title="variable">xc</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#14a7a9c7dc61f86bfb664d400fabaf8a"><span class="id" title="notation">)</span></a><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#14a7a9c7dc61f86bfb664d400fabaf8a"><span class="id" title="notation">||</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#14a7a9c7dc61f86bfb664d400fabaf8a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bc"><span class="id" title="variable">bc</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xc"><span class="id" title="variable">xc</span></a>) <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#14a7a9c7dc61f86bfb664d400fabaf8a"><span class="id" title="notation">)</span></a>.<br/>
+<span class="id" title="keyword">Canonical</span> <span class="id" title="var">itv_intersection_monoid</span> :=<br/>
+&nbsp;&nbsp;<a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Law"><span class="id" title="constructor">Monoid.Law</span></a> <a class="idref" href="mathcomp.algebra.interval.html#itv_intersectionA"><span class="id" title="lemma">itv_intersectionA</span></a> (@<a class="idref" href="mathcomp.algebra.interval.html#itv_intersection1i"><span class="id" title="definition">itv_intersection1i</span></a> <a class="idref" href="mathcomp.algebra.interval.html#IntervalOrdered.R"><span class="id" title="variable">R</span></a>) (@<a class="idref" href="mathcomp.algebra.interval.html#itv_intersectioni1"><span class="id" title="definition">itv_intersectioni1</span></a> <a class="idref" href="mathcomp.algebra.interval.html#IntervalOrdered.R"><span class="id" title="variable">R</span></a>).<br/>
 
 <br/>
-<span class="id" title="keyword">Lemma</span> <a name="itv_splitU2"><span class="id" title="lemma">itv_splitU2</span></a> (<span class="id" title="var">x</span> : <a class="idref" href="mathcomp.algebra.interval.html#IntervalOrdered.R"><span class="id" title="variable">R</span></a>) <span class="id" title="var">a</span> <span class="id" title="var">b</span> : <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a><br/>
-&nbsp;&nbsp;<span class="id" title="keyword">∀</span> <span class="id" title="var">y</span>, <a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">=</span></a><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">[||</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> <a class="idref" href="mathcomp.algebra.interval.html#a"><span class="id" title="variable">a</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen"><span class="id" title="abbreviation">BOpen</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">),</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">)</span></a><br/>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen"><span class="id" title="abbreviation">BOpen</span></a> <a class="idref" href="mathcomp.algebra.interval.html#x"><span class="id" title="variable">x</span></a>) <a class="idref" href="mathcomp.algebra.interval.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#61dc88e70df6fc30a5b49c217ac7b79d"><span class="id" title="notation">)]</span></a>.<br/>
+<span class="id" title="keyword">Canonical</span> <span class="id" title="var">itv_intersection_comoid</span> := <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.ComLaw"><span class="id" title="constructor">Monoid.ComLaw</span></a> <a class="idref" href="mathcomp.algebra.interval.html#itv_intersectionC"><span class="id" title="lemma">itv_intersectionC</span></a>.<br/>
 
 <br/>
 <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.interval.html#IntervalOrdered"><span class="id" title="section">IntervalOrdered</span></a>.<br/>
@@ -401,14 +637,14 @@
 <span class="id" title="keyword">Variable</span> <a name="IntervalField.R"><span class="id" title="variable">R</span></a> : <a class="idref" href="mathcomp.algebra.ssrnum.html#Num.RealField.Exports.realFieldType"><span class="id" title="abbreviation">realFieldType</span></a>.<br/>
 
 <br/>
-<span class="id" title="keyword">Lemma</span> <a name="mid_in_itv"><span class="id" title="lemma">mid_in_itv</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">ba</span> <span class="id" title="var">bb</span> (<span class="id" title="var">xa</span> <span class="id" title="var">xb</span> : <a class="idref" href="mathcomp.algebra.interval.html#IntervalField.R"><span class="id" title="variable">R</span></a>), <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bec03331256891011ac5a0ab95580e68"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bec03331256891011ac5a0ab95580e68"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bec03331256891011ac5a0ab95580e68"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bec03331256891011ac5a0ab95580e68"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.algebra.interval.html#ba"><span class="id" title="variable">ba</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#14a7a9c7dc61f86bfb664d400fabaf8a"><span class="id" title="notation">||</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bb"><span class="id" title="variable">bb</span></a><a class="idref" href="mathcomp.algebra.interval.html#bec03331256891011ac5a0ab95580e68"><span class="id" title="notation">)</span></a><br/>
-&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#mid"><span class="id" title="abbreviation">mid</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#ba"><span class="id" title="variable">ba</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a>) (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bb"><span class="id" title="variable">bb</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a>).<br/>
+<span class="id" title="keyword">Lemma</span> <a name="mid_in_itv"><span class="id" title="lemma">mid_in_itv</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">ba</span> <span class="id" title="var">bb</span> (<span class="id" title="var">xa</span> <span class="id" title="var">xb</span> : <a class="idref" href="mathcomp.algebra.interval.html#IntervalField.R"><span class="id" title="variable">R</span></a>), <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">?&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2bafcba5e020e03f24077f5d83dfd2f0"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#ba"><span class="id" title="variable">ba</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">||</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bb"><span class="id" title="variable">bb</span></a><br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#mid"><span class="id" title="abbreviation">mid</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#Interval"><span class="id" title="constructor">Interval</span></a> (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#ba"><span class="id" title="variable">ba</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a>) (<a class="idref" href="mathcomp.algebra.interval.html#BOpen_if"><span class="id" title="constructor">BOpen_if</span></a> <a class="idref" href="mathcomp.algebra.interval.html#bb"><span class="id" title="variable">bb</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a>).<br/>
 
 <br/>
-<span class="id" title="keyword">Lemma</span> <a name="mid_in_itvoo"><span class="id" title="lemma">mid_in_itvoo</span></a> : <span class="id" title="keyword">∀</span> (<span class="id" title="var">xa</span> <span class="id" title="var">xb</span> : <a class="idref" href="mathcomp.algebra.interval.html#IntervalField.R"><span class="id" title="variable">R</span></a>), <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#388c172bf8d34ef0bf11898cd56f8d7b"><span class="id" title="notation">&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#mid"><span class="id" title="abbreviation">mid</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#2e8617f61b689dc49fc99a5898babaf3"><span class="id" title="notation">`]</span></a><a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a><a class="idref" href="mathcomp.algebra.interval.html#2e8617f61b689dc49fc99a5898babaf3"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a><a class="idref" href="mathcomp.algebra.interval.html#2e8617f61b689dc49fc99a5898babaf3"><span class="id" title="notation">[</span></a>.<br/>
+<span class="id" title="keyword">Lemma</span> <a name="mid_in_itvoo"><span class="id" title="lemma">mid_in_itvoo</span></a> : <span class="id" title="keyword">∀</span> (<span class="id" title="var">xa</span> <span class="id" title="var">xb</span> : <a class="idref" href="mathcomp.algebra.interval.html#IntervalField.R"><span class="id" title="variable">R</span></a>), <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#eb5186e6835d7e27cbb4c691b2f398bb"><span class="id" title="notation">&lt;</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#mid"><span class="id" title="abbreviation">mid</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#ebff9f8c4fe58806999ff1c12ccee445"><span class="id" title="notation">`]</span></a><a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a><a class="idref" href="mathcomp.algebra.interval.html#ebff9f8c4fe58806999ff1c12ccee445"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a><a class="idref" href="mathcomp.algebra.interval.html#ebff9f8c4fe58806999ff1c12ccee445"><span class="id" title="notation">[</span></a>.<br/>
  
 <br/>
-<span class="id" title="keyword">Lemma</span> <a name="mid_in_itvcc"><span class="id" title="lemma">mid_in_itvcc</span></a> : <span class="id" title="keyword">∀</span> (<span class="id" title="var">xa</span> <span class="id" title="var">xb</span> : <a class="idref" href="mathcomp.algebra.interval.html#IntervalField.R"><span class="id" title="variable">R</span></a>), <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#1065783963a393d1eafa2137291f2495"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#mid"><span class="id" title="abbreviation">mid</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#46c9e8232fa09401e24f1934bb65029f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#1b23dabf87b87c155f5c39a03cf252fd"><span class="id" title="notation">`[</span></a><a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a><a class="idref" href="mathcomp.algebra.interval.html#1b23dabf87b87c155f5c39a03cf252fd"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a><a class="idref" href="mathcomp.algebra.interval.html#1b23dabf87b87c155f5c39a03cf252fd"><span class="id" title="notation">]</span></a>.<br/>
+<span class="id" title="keyword">Lemma</span> <a name="mid_in_itvcc"><span class="id" title="lemma">mid_in_itvcc</span></a> : <span class="id" title="keyword">∀</span> (<span class="id" title="var">xa</span> <span class="id" title="var">xb</span> : <a class="idref" href="mathcomp.algebra.interval.html#IntervalField.R"><span class="id" title="variable">R</span></a>), <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a> <a class="idref" href="mathcomp.algebra.ssrnum.html#cb42ec59ad57b25928e1718b4e69e031"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.algebra.interval.html#mid"><span class="id" title="abbreviation">mid</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">`[</span></a><a class="idref" href="mathcomp.algebra.interval.html#xa"><span class="id" title="variable">xa</span></a><a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.algebra.interval.html#xb"><span class="id" title="variable">xb</span></a><a class="idref" href="mathcomp.algebra.interval.html#3faa329f2bb2903beba94067ccb07f1b"><span class="id" title="notation">]</span></a>.<br/>
  
 <br/>
 <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.algebra.interval.html#IntervalField"><span class="id" title="section">IntervalField</span></a>.<br/>