generate the documentation for 1.7

author: Enrico Tassi 2018-04-20 10:54:22 +0200
committer: Enrico Tassi 2018-04-20 10:54:22 +0200
commit: ed05182cece6bb3706e09b2ce14af4a41a2e8141 (patch)
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+<div id="main">
+
+<h1 class="libtitle">Library mathcomp.ssreflect.eqtype</h1>
+
+<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>
+
+<div class="doc">
+ This file defines two "base" combinatorial interfaces:                     
+    eqType == the structure for types with a decidable equality.            
+              Equality mixins can be made Canonical to allow generic        
+              folding of equality predicates.                               
+ subType p == the structure for types isomorphic to {x : T | p x} with      
+              p : pred T for some type T.                                   
+ The eqType interface supports the following operations:                    
+          x == y &lt;=&gt; x compares equal to y (this is a boolean test).        
+     x == y :&gt; T &lt;=&gt; x == y at type T.                                      
+          x != y &lt;=&gt; x and y compare unequal.                               
+     x != y :&gt; T &lt;=&gt;  "    "      "    "     at type T.                     
+         x =P y  :: a proof of reflect (x = y) (x == y); this coerces       
+                     to x == y -&gt; x = y.                                    
+    comparable T &lt;-&gt; equality on T is decidable                             
+                    := forall x y : T, decidable (x = y)                    
+  comparableClass compT == eqType mixin/class for compT : comparable T.     
+             pred1 a == the singleton predicate [pred x | x == a].          
+ pred2, pred3, pred4 == pair, triple, quad predicates.                      
+            predC1 a == [pred x | x != a].                                  
+      [predU1 a &amp; A] == [pred x | (x == a) || (x \in A) ].                   
+      [predD1 A &amp; a] == [pred x | x != a &amp; x \in A].                        
+  predU1 a P, predD1 P a == applicative versions of the above.              
+              frel f == the relation associated with f : T -&gt; T.            
+                     := [rel x y | f x == y].                               
+       invariant k f == elements of T whose k-class is f-invariant.         
+                     := [pred x | k (f x) == k x] with f : T -&gt; T.          
+  [fun x : T =&gt; e0 with a1 |-&gt; e1, .., a_n |-&gt; e_n]                         
+  [eta f with a1 |-&gt; e1, .., a_n |-&gt; e_n] ==                                
+    the auto-expanding function that maps x = a_i to e_i, and other values  
+    of x to e0 (resp. f x). In the first form the `: T' is optional and x   
+    can occur in a_i or e_i.                                                
+ Equality on an eqType is proof-irrelevant (lemma eq_irrelevance).          
+   The eqType interface is implemented for most standard datatypes:         
+  bool, unit, void, option, prod (denoted A * B), sum (denoted A + B),      
+  sig (denoted {x | P}), sigT (denoted {i : I &amp; T}). We also define         
+   tagged_as u v == v cast as T(tag u) if tag v == tag u, else u.          
+<ul class="doclist">
+<li>&gt; We have u == v &lt;=&gt; (tag u == tag v) &amp;&amp; (tagged u == tagged_as u v).    
+
+</li>
+</ul>
+ The subType interface supports the following operations:                   
+      val == the generic injection from a subType S of T into T.            
+             For example, if u : {x : T | P}, then val u : T.               
+             val is injective because P is proof-irrelevant (P is in bool,  
+             and the is_true coercion expands to P = true).                 
+     valP == the generic proof of P (val u) for u : subType P.              
+ Sub x Px == the generic constructor for a subType P; Px is a proof of P x  
+             and P should be inferred from the expected return type.        
+  insub x == the generic partial projection of T into a subType S of T.     
+             This returns an option S; if S : subType P then                
+                insub x = Some u with val u = x if P x,                     
+                          None if ~~ P x                                    
+             The insubP lemma encapsulates this dichotomy.                  
+             P should be infered from the expected return type.             
+  innew x == total (non-option) variant of insub when P = predT.            
+ {? x | P} == option {x | P} (syntax for casting insub x).                  
+ insubd u0 x == the generic projection with default value u0.               
+             := odflt u0 (insub x).                                         
+ insigd A0 x == special case of insubd for S == {x | x \in A}, where A0 is  
+                a proof of x0 \in A.                                        
+ insub_eq x == transparent version of insub x that expands to Some/None     
+               when P x can evaluate.                                       
+  The subType P interface is most often implemented using one of:           
+   [subType for S_val]                                                      
+     where S_val : S -&gt; T is the first projection of a type S isomorphic to 
+     {x : T | P}.                                                           
+   [newType for S_val]                                                      
+     where S_val : S -&gt; T is the projection of a type S isomorphic to       
+     wrapped T; in this case P must be predT.                               
+   [subType for S_val by Srect], [newType for S_val by Srect]               
+     variants of the above where the eliminator is explicitly provided.     
+     Here S no longer needs to be syntactically identical to {x | P x} or   
+     wrapped T, but it must have a derived constructor S_Sub statisfying an 
+     eliminator Srect identical to the one the Coq Inductive command would  
+     have generated, and S_val (S_Sub x Px) (resp. S_val (S_sub x) for the  
+     newType form) must be convertible to x.                                
+     variant of the above when S is a wrapper type for T (so P = predT).    
+   [subType of S], [subType of S for S_val]                                 
+     clones the canonical subType structure for S; if S_val is specified,   
+     then it replaces the inferred projector.                               
+ Subtypes inherit the eqType structure of their base types; the generic     
+ structure should be explicitly instantiated using the                      
+   [eqMixin of S by &lt;: ]                                                     
+ construct to declare the Equality mixin; this pattern is repeated for all  
+ the combinatorial interfaces (Choice, Countable, Finite).                  
+   More generally, the eqType structure can be transfered by (partial)      
+ injections, using:                                                         
+   InjEqMixin injf == an Equality mixin for T, using an f : T -&gt; eT where   
+                      eT has an eqType structure and injf : injective f.    
+    PcanEqMixin fK == an Equality mixin similarly derived from f and a left 
+                      inverse partial function g and fK : pcancel f g.      
+     CanEqMixin fK == an Equality mixin similarly derived from f and a left 
+                      inverse function g and fK : cancel f g.               
+   We add the following to the standard suffixes documented in ssrbool.v:   
+  1, 2, 3, 4 -- explicit enumeration predicate for 1 (singleton), 2, 3, or  
+                4 values.                                                    
+</div>
+<div class="code">
+
+<br/>
+<span class="id" title="keyword">Set Implicit Arguments</span>.<br/>
+
+<br/>
+<span class="id" title="keyword">Module</span> <a name="Equality"><span class="id" title="module">Equality</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="Equality.axiom"><span class="id" title="definition">axiom</span></a> <span class="id" title="var">T</span> (<span class="id" title="var">e</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#rel"><span class="id" title="definition">rel</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#T"><span class="id" title="variable">T</span></a>) := <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span>, <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.ssreflect.eqtype.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="mathcomp.ssreflect.eqtype.html#y"><span class="id" title="variable">y</span></a>) (<a class="idref" href="mathcomp.ssreflect.eqtype.html#e"><span class="id" title="variable">e</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#y"><span class="id" title="variable">y</span></a>).<br/>
+
+<br/>
+<span class="id" title="keyword">Structure</span> <a name="Equality.mixin_of"><span class="id" title="record">mixin_of</span></a> <span class="id" title="var">T</span> := <a name="Equality.Mixin"><span class="id" title="constructor">Mixin</span></a> {<a name="Equality.op"><span class="id" title="projection">op</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#rel"><span class="id" title="definition">rel</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#T"><span class="id" title="variable">T</span></a>; <span class="id" title="var">_</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.axiom"><span class="id" title="definition">axiom</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#op"><span class="id" title="method">op</span></a>}.<br/>
+<span class="id" title="keyword">Notation</span> <a name="Equality.class_of"><span class="id" title="abbreviation">class_of</span></a> := <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.mixin_of"><span class="id" title="record">mixin_of</span></a> (<span class="id" title="var">only</span> <span class="id" title="var">parsing</span>).<br/>
+
+<br/>
+<span class="id" title="keyword">Section</span> <a name="Equality.ClassDef"><span class="id" title="section">ClassDef</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Structure</span> <a name="Equality.type"><span class="id" title="record">type</span></a> := <a name="Equality.Pack"><span class="id" title="constructor">Pack</span></a> {<a name="Equality.sort"><span class="id" title="projection">sort</span></a>; <span class="id" title="var">_</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.class_of"><span class="id" title="abbreviation">class_of</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#sort"><span class="id" title="method">sort</span></a>; <span class="id" title="var">_</span> : <span class="id" title="keyword">Type</span>}.<br/>
+<span class="id" title="keyword">Variables</span> (<a name="Equality.ClassDef.T"><span class="id" title="variable">T</span></a> : <span class="id" title="keyword">Type</span>) (<a name="Equality.ClassDef.cT"><span class="id" title="variable">cT</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.type"><span class="id" title="record">type</span></a>).<br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="Equality.class"><span class="id" title="definition">class</span></a> := <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Pack"><span class="id" title="constructor">Pack</span></a> <span class="id" title="var">_</span> <span class="id" title="var">c</span> <span class="id" title="var">_</span> := <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.ClassDef.cT"><span class="id" title="variable">cT</span></a> <span class="id" title="keyword">return</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.class_of"><span class="id" title="abbreviation">class_of</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#cT"><span class="id" title="variable">cT</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">c</span>.<br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="Equality.pack"><span class="id" title="definition">pack</span></a> <span class="id" title="var">c</span> := @<a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Pack"><span class="id" title="constructor">Pack</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.ClassDef.T"><span class="id" title="variable">T</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c"><span class="id" title="variable">c</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.ClassDef.T"><span class="id" title="variable">T</span></a>.<br/>
+<span class="id" title="keyword">Definition</span> <a name="Equality.clone"><span class="id" title="definition">clone</span></a> := <span class="id" title="keyword">fun</span> <span class="id" title="var">c</span> &amp; <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.ClassDef.cT"><span class="id" title="variable">cT</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.ssreflect.eqtype.html#Equality.ClassDef.T"><span class="id" title="variable">T</span></a> &amp; <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#phant_id"><span class="id" title="definition">phant_id</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.pack"><span class="id" title="definition">pack</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c"><span class="id" title="variable">c</span></a>) <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.ClassDef.cT"><span class="id" title="variable">cT</span></a> ⇒ <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.pack"><span class="id" title="definition">pack</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c"><span class="id" title="variable">c</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.ClassDef"><span class="id" title="section">ClassDef</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Module</span> <a name="Equality.Exports"><span class="id" title="module">Exports</span></a>.<br/>
+<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.sort"><span class="id" title="projection">sort</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.sort"><span class="id" title="projection">:</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.sort"><span class="id" title="projection">type</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.sort"><span class="id" title="projection">&gt;-&gt;</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.sort"><span class="id" title="projection">Sortclass</span></a>.<br/>
+<span class="id" title="keyword">Notation</span> <a name="Equality.Exports.eqType"><span class="id" title="abbreviation">eqType</span></a> := <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.type"><span class="id" title="record">type</span></a>.<br/>
+<span class="id" title="keyword">Notation</span> <a name="Equality.Exports.EqMixin"><span class="id" title="abbreviation">EqMixin</span></a> := <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Mixin"><span class="id" title="constructor">Mixin</span></a>.<br/>
+<span class="id" title="keyword">Notation</span> <a name="Equality.Exports.EqType"><span class="id" title="abbreviation">EqType</span></a> <span class="id" title="var">T</span> <span class="id" title="var">m</span> := (@<a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.pack"><span class="id" title="definition">pack</span></a> <span class="id" title="var">T</span> <span class="id" title="var">m</span>).<br/>
+<span class="id" title="keyword">Notation</span> <a name="78287ce0666bcaa587a668e46d5a01f3"><span class="id" title="notation">&quot;</span></a>[ 'eqMixin' 'of' T ]" := (<a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.class"><span class="id" title="definition">class</span></a> <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#4509b22bf26e3d6d771897e22bd8bc8f"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.mixin_of"><span class="id" title="record">mixin_of</span></a> <span class="id" title="var">T</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> "[ 'eqMixin'  'of'  T ]") : <span class="id" title="var">form_scope</span>.<br/>
+<span class="id" title="keyword">Notation</span> <a name="ea28a4d33dfb78a62dc4071e70f3d5db"><span class="id" title="notation">&quot;</span></a>[ 'eqType' 'of' T 'for' C ]" := (@<a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.clone"><span class="id" title="definition">clone</span></a> <span class="id" title="var">T</span> <span class="id" title="var">C</span> <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#idfun"><span class="id" title="abbreviation">idfun</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a>)<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> "[ 'eqType'  'of'  T  'for'  C ]") : <span class="id" title="var">form_scope</span>.<br/>
+<span class="id" title="keyword">Notation</span> <a name="cb062fd562aed512787df99359c6e3f2"><span class="id" title="notation">&quot;</span></a>[ 'eqType' 'of' T ]" := (@<a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.clone"><span class="id" title="definition">clone</span></a> <span class="id" title="var">T</span> <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.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a>)<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> "[ 'eqType'  'of'  T ]") : <span class="id" title="var">form_scope</span>.<br/>
+<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Exports"><span class="id" title="module">Exports</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality"><span class="id" title="module">Equality</span></a>.<br/>
+<span class="id" title="keyword">Export</span> <span class="id" title="var">Equality.Exports</span>.<br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="eq_op"><span class="id" title="definition">eq_op</span></a> <span class="id" title="var">T</span> := <a class="idref" href="mathcomp.ssreflect.eqtype.html#op"><span class="id" title="projection">Equality.op</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#class"><span class="id" title="definition">Equality.class</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#T"><span class="id" title="variable">T</span></a>).<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="eqE"><span class="id" title="lemma">eqE</span></a> <span class="id" title="var">T</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#eq_op"><span class="id" title="definition">eq_op</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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="mathcomp.ssreflect.eqtype.html#op"><span class="id" title="projection">Equality.op</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#class"><span class="id" title="definition">Equality.class</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#T"><span class="id" title="variable">T</span></a>) <a class="idref" href="mathcomp.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="eqP"><span class="id" title="lemma">eqP</span></a> <span class="id" title="var">T</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#axiom"><span class="id" title="definition">Equality.axiom</span></a> (@<a class="idref" href="mathcomp.ssreflect.eqtype.html#eq_op"><span class="id" title="definition">eq_op</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#T"><span class="id" title="variable">T</span></a>).<br/>
+ 
+<br/>
+<span class="id" title="keyword">Delimit</span> <span class="id" title="keyword">Scope</span> <span class="id" title="var">eq_scope</span> <span class="id" title="keyword">with</span> <span class="id" title="var">EQ</span>.<br/>
+<span class="id" title="keyword">Open</span> <span class="id" title="keyword">Scope</span> <span class="id" title="var">eq_scope</span>.<br/>
+
+<br/>
+<span class="id" title="keyword">Notation</span> <a name="17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">&quot;</span></a>x == y" := (<a class="idref" href="mathcomp.ssreflect.eqtype.html#eq_op"><span class="id" title="definition">eq_op</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span>)<br/>
+&nbsp;&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 70, <span class="id" title="keyword">no</span> <span class="id" title="keyword">associativity</span>) : <span class="id" title="var">bool_scope</span>.<br/>
+<span class="id" title="keyword">Notation</span> <a name="340b60eb5a3e9913f807040630cb8d43"><span class="id" title="notation">&quot;</span></a>x == y :&gt; T" := (<a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">(</span></a><span class="id" title="var">x</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#4509b22bf26e3d6d771897e22bd8bc8f"><span class="id" title="notation">:</span></a> <span class="id" title="var">T</span><a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">(</span></a><span class="id" title="var">y</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#4509b22bf26e3d6d771897e22bd8bc8f"><span class="id" title="notation">:</span></a> <span class="id" title="var">T</span><a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">)</span></a>)<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>) : <span class="id" title="var">bool_scope</span>.<br/>
+<span class="id" title="keyword">Notation</span> <a name="b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">&quot;</span></a>x != y" := (<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><span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <span class="id" title="var">y</span><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;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 70, <span class="id" title="keyword">no</span> <span class="id" title="keyword">associativity</span>) : <span class="id" title="var">bool_scope</span>.<br/>
+<span class="id" title="keyword">Notation</span> <a name="9e45f909d1732d6d9e153b650829bccf"><span class="id" title="notation">&quot;</span></a>x != y :&gt; T" := (<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><span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#340b60eb5a3e9913f807040630cb8d43"><span class="id" title="notation">==</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#340b60eb5a3e9913f807040630cb8d43"><span class="id" title="notation">:&gt;</span></a> <span class="id" title="var">T</span><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;(<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>) : <span class="id" title="var">bool_scope</span>.<br/>
+<span class="id" title="keyword">Notation</span> <a name="ab7a7bc39754581ab8f205db64711d57"><span class="id" title="notation">&quot;</span></a>x =P y" := (<a class="idref" href="mathcomp.ssreflect.eqtype.html#eqP"><span class="id" title="lemma">eqP</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#4509b22bf26e3d6d771897e22bd8bc8f"><span class="id" title="notation">:</span></a> <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> (<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> <span class="id" title="var">y</span>) (<span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <span class="id" title="var">y</span>))<br/>
+&nbsp;&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 70, <span class="id" title="keyword">no</span> <span class="id" title="keyword">associativity</span>) : <span class="id" title="var">eq_scope</span>.<br/>
+<span class="id" title="keyword">Notation</span> <a name="57fb9faa34beea4ffe4cd740203a17ea"><span class="id" title="notation">&quot;</span></a>x =P y :&gt; T" := (<a class="idref" href="mathcomp.ssreflect.eqtype.html#eqP"><span class="id" title="lemma">eqP</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#4509b22bf26e3d6d771897e22bd8bc8f"><span class="id" title="notation">:</span></a> <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> (<span class="id" title="var">x</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#8f9364556521ebb498093f28eea2240f"><span class="id" title="notation">=</span></a> <span class="id" title="var">y</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#8f9364556521ebb498093f28eea2240f"><span class="id" title="notation">:&gt;</span></a> <span class="id" title="var">T</span>) (<span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#340b60eb5a3e9913f807040630cb8d43"><span class="id" title="notation">==</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#340b60eb5a3e9913f807040630cb8d43"><span class="id" title="notation">:&gt;</span></a> <span class="id" title="var">T</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>, <span class="id" title="keyword">no</span> <span class="id" title="keyword">associativity</span>) : <span class="id" title="var">eq_scope</span>.<br/>
+
+<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="eq_refl"><span class="id" title="lemma">eq_refl</span></a> (<span class="id" title="var">T</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#eqType"><span class="id" title="abbreviation">eqType</span></a>) (<span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#T"><span class="id" title="variable">T</span></a>) : <a class="idref" href="mathcomp.ssreflect.eqtype.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.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a>.  <br/>
+<span class="id" title="keyword">Notation</span> <a name="eqxx"><span class="id" title="abbreviation">eqxx</span></a> := <a class="idref" href="mathcomp.ssreflect.eqtype.html#eq_refl"><span class="id" title="lemma">eq_refl</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="eq_sym"><span class="id" title="lemma">eq_sym</span></a> (<span class="id" title="var">T</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#eqType"><span class="id" title="abbreviation">eqType</span></a>) (<span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#T"><span class="id" title="variable">T</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.ssreflect.eqtype.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.ssreflect.eqtype.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> <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.ssreflect.eqtype.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.ssreflect.eqtype.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/>
+ 
+<br/>
+<span class="id" title="keyword">Hint Resolve</span> <span class="id" title="var">eq_refl</span> <span class="id" title="var">eq_sym</span>.<br/>
+
+<br/>
+<span class="id" title="keyword">Section</span> <a name="Contrapositives"><span class="id" title="section">Contrapositives</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Variables</span> (<a name="Contrapositives.T1"><span class="id" title="variable">T1</span></a> <a name="Contrapositives.T2"><span class="id" title="variable">T2</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#eqType"><span class="id" title="abbreviation">eqType</span></a>).<br/>
+<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> (<span class="id" title="var">A</span> : <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.ssreflect.eqtype.html#Contrapositives.T1"><span class="id" title="variable">T1</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#bool"><span class="id" title="inductive">bool</span></a>) (<span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#Contrapositives.T1"><span class="id" title="variable">T1</span></a>) (<span class="id" title="var">z</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#Contrapositives.T2"><span class="id" title="variable">T2</span></a>).<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="contraTeq"><span class="id" title="lemma">contraTeq</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="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.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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="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.ssreflect.eqtype.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="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.ssreflect.eqtype.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.ssreflect.eqtype.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="mathcomp.ssreflect.eqtype.html#y"><span class="id" title="variable">y</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="contraNeq"><span class="id" title="lemma">contraNeq</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="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.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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.ssreflect.eqtype.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="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#4b80c70cdb231351c5e129ba61f7f956"><span class="id" title="notation">~~</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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.ssreflect.eqtype.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="mathcomp.ssreflect.eqtype.html#y"><span class="id" title="variable">y</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="contraFeq"><span class="id" title="lemma">contraFeq</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="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.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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.ssreflect.eqtype.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="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.ssreflect.eqtype.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> <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.ssreflect.eqtype.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="mathcomp.ssreflect.eqtype.html#y"><span class="id" title="variable">y</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="contraTneq"><span class="id" title="lemma">contraTneq</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="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.ssreflect.eqtype.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="mathcomp.ssreflect.eqtype.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="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.ssreflect.eqtype.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="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.ssreflect.eqtype.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.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#y"><span class="id" title="variable">y</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="contraNneq"><span class="id" title="lemma">contraNneq</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="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.ssreflect.eqtype.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="mathcomp.ssreflect.eqtype.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.ssreflect.eqtype.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="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#4b80c70cdb231351c5e129ba61f7f956"><span class="id" title="notation">~~</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#y"><span class="id" title="variable">y</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="contraFneq"><span class="id" title="lemma">contraFneq</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="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.ssreflect.eqtype.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="mathcomp.ssreflect.eqtype.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.ssreflect.eqtype.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="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.ssreflect.eqtype.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> <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.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#y"><span class="id" title="variable">y</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="contra_eqN"><span class="id" title="lemma">contra_eqN</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="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.ssreflect.eqtype.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.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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="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.ssreflect.eqtype.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="mathcomp.ssreflect.eqtype.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="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.ssreflect.eqtype.html#b"><span class="id" title="variable">b</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="contra_eqF"><span class="id" title="lemma">contra_eqF</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="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.ssreflect.eqtype.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.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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="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.ssreflect.eqtype.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="mathcomp.ssreflect.eqtype.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.ssreflect.eqtype.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="contra_eqT"><span class="id" title="lemma">contra_eqT</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="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#4b80c70cdb231351c5e129ba61f7f956"><span class="id" title="notation">~~</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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="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.ssreflect.eqtype.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="mathcomp.ssreflect.eqtype.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.ssreflect.eqtype.html#b"><span class="id" title="variable">b</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="contra_eq"><span class="id" title="lemma">contra_eq</span></a> <span class="id" title="var">z1</span> <span class="id" title="var">z2</span> <span class="id" title="var">x1</span> <span class="id" title="var">x2</span> : <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.ssreflect.eqtype.html#x1"><span class="id" title="variable">x1</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#x2"><span class="id" title="variable">x2</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.ssreflect.eqtype.html#z1"><span class="id" title="variable">z1</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#z2"><span class="id" title="variable">z2</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.ssreflect.eqtype.html#z1"><span class="id" title="variable">z1</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.ssreflect.eqtype.html#z2"><span class="id" title="variable">z2</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.ssreflect.eqtype.html#x1"><span class="id" title="variable">x1</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.ssreflect.eqtype.html#x2"><span class="id" title="variable">x2</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="contra_neq"><span class="id" title="lemma">contra_neq</span></a> <span class="id" title="var">z1</span> <span class="id" title="var">z2</span> <span class="id" title="var">x1</span> <span class="id" title="var">x2</span> : <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.ssreflect.eqtype.html#x1"><span class="id" title="variable">x1</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.ssreflect.eqtype.html#x2"><span class="id" title="variable">x2</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.ssreflect.eqtype.html#z1"><span class="id" title="variable">z1</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.ssreflect.eqtype.html#z2"><span class="id" title="variable">z2</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.ssreflect.eqtype.html#z1"><span class="id" title="variable">z1</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#z2"><span class="id" title="variable">z2</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.ssreflect.eqtype.html#x1"><span class="id" title="variable">x1</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#x2"><span class="id" title="variable">x2</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="memPn"><span class="id" title="lemma">memPn</span></a> <span class="id" title="var">A</span> <span class="id" title="var">x</span> : <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="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">y</span>, <a class="idref" href="mathcomp.ssreflect.eqtype.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">}</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.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#ad6d23746eb1a3b62e52010d3945a1db"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ad6d23746eb1a3b62e52010d3945a1db"><span class="id" title="notation">notin</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#A"><span class="id" title="variable">A</span></a>).<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="memPnC"><span class="id" title="lemma">memPnC</span></a> <span class="id" title="var">A</span> <span class="id" title="var">x</span> : <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="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">y</span>, <a class="idref" href="mathcomp.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">}</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.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#ad6d23746eb1a3b62e52010d3945a1db"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#ad6d23746eb1a3b62e52010d3945a1db"><span class="id" title="notation">notin</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#A"><span class="id" title="variable">A</span></a>).<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="ifN_eq"><span class="id" title="lemma">ifN_eq</span></a> <span class="id" title="var">R</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <span class="id" title="var">vT</span> <span class="id" title="var">vF</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#8f9364556521ebb498093f28eea2240f"><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">if</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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.ssreflect.eqtype.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">then</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#vT"><span class="id" title="variable">vT</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.ssreflect.eqtype.html#vF"><span class="id" title="variable">vF</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#8f9364556521ebb498093f28eea2240f"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#8f9364556521ebb498093f28eea2240f"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#vF"><span class="id" title="variable">vF</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#8f9364556521ebb498093f28eea2240f"><span class="id" title="notation">:&gt;</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#R"><span class="id" title="variable">R</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="ifN_eqC"><span class="id" title="lemma">ifN_eqC</span></a> <span class="id" title="var">R</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <span class="id" title="var">vT</span> <span class="id" title="var">vF</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#8f9364556521ebb498093f28eea2240f"><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">if</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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.ssreflect.eqtype.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">then</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#vT"><span class="id" title="variable">vT</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.ssreflect.eqtype.html#vF"><span class="id" title="variable">vF</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#8f9364556521ebb498093f28eea2240f"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#8f9364556521ebb498093f28eea2240f"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#vF"><span class="id" title="variable">vF</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#8f9364556521ebb498093f28eea2240f"><span class="id" title="notation">:&gt;</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#R"><span class="id" title="variable">R</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#Contrapositives"><span class="id" title="section">Contrapositives</span></a>.<br/>
+
+<br/>
+
+<br/>
+<span class="id" title="keyword">Theorem</span> <a name="eq_irrelevance"><span class="id" title="lemma">eq_irrelevance</span></a> (<span class="id" title="var">T</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#eqType"><span class="id" title="abbreviation">eqType</span></a>) <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <span class="id" title="keyword">∀</span> <span class="id" title="var">e1</span> <span class="id" title="var">e2</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.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#8f9364556521ebb498093f28eea2240f"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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#8f9364556521ebb498093f28eea2240f"><span class="id" title="notation">:&gt;</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#T"><span class="id" title="variable">T</span></a>, <a class="idref" href="mathcomp.ssreflect.eqtype.html#e1"><span class="id" title="variable">e1</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.ssreflect.eqtype.html#e2"><span class="id" title="variable">e2</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Corollary</span> <a name="eq_axiomK"><span class="id" title="lemma">eq_axiomK</span></a> (<span class="id" title="var">T</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#eqType"><span class="id" title="abbreviation">eqType</span></a>) (<span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#T"><span class="id" title="variable">T</span></a>) : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#all_equal_to"><span class="id" title="definition">all_equal_to</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#erefl"><span class="id" title="abbreviation">erefl</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a>).<br/>
+ 
+<br/>
+</div>
+
+<div class="doc">
+ We use the module system to circumvent a silly limitation that  
+ forbids using the same constant to coerce to different targets.  
+</div>
+<div class="code">
+<span class="id" title="keyword">Module</span> <span class="id" title="keyword">Type</span> <a name="EqTypePredSig"><span class="id" title="module">EqTypePredSig</span></a>.<br/>
+<span class="id" title="keyword">Parameter</span> <a name="EqTypePredSig.sort"><span class="id" title="axiom">sort</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Exports.eqType"><span class="id" title="abbreviation">eqType</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#predArgType"><span class="id" title="definition">predArgType</span></a>.<br/>
+<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqTypePredSig"><span class="id" title="module">EqTypePredSig</span></a>.<br/>
+<span class="id" title="keyword">Module</span> <a name="MakeEqTypePred"><span class="id" title="module">MakeEqTypePred</span></a> (<span class="id" title="var">eqmod</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqTypePredSig"><span class="id" title="module">EqTypePredSig</span></a>).<br/>
+<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#eqmod.sort"><span class="id" title="axiom">eqmod.sort</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#eqmod.sort"><span class="id" title="axiom">:</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#eqmod.sort"><span class="id" title="axiom">eqType</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#eqmod.sort"><span class="id" title="axiom">&gt;-&gt;</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#eqmod.sort"><span class="id" title="axiom">predArgType</span></a>.<br/>
+<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#MakeEqTypePred"><span class="id" title="module">MakeEqTypePred</span></a>.<br/>
+<span class="id" title="keyword">Module</span> <span class="id" title="keyword">Export</span> <a name="EqTypePred"><span class="id" title="module">EqTypePred</span></a> := <a class="idref" href="mathcomp.ssreflect.eqtype.html#MakeEqTypePred"><span class="id" title="module">MakeEqTypePred</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality"><span class="id" title="module">Equality</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="unit_eqP"><span class="id" title="lemma">unit_eqP</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#axiom"><span class="id" title="definition">Equality.axiom</span></a> (<span class="id" title="keyword">fun</span> <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#unit"><span class="id" title="inductive">unit</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/>
+ 
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="unit_eqMixin"><span class="id" title="definition">unit_eqMixin</span></a> := <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqMixin"><span class="id" title="abbreviation">EqMixin</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#unit_eqP"><span class="id" title="lemma">unit_eqP</span></a>.<br/>
+<span class="id" title="keyword">Canonical</span> <span class="id" title="var">unit_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#EqType"><span class="id" title="abbreviation">EqType</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#unit"><span class="id" title="inductive">unit</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#unit_eqMixin"><span class="id" title="definition">unit_eqMixin</span></a>.<br/>
+
+<br/>
+</div>
+
+<div class="doc">
+ Comparison for booleans.  
+<div class="paragraph"> </div>
+
+  This is extensionally equal, but not convertible to Bool.eqb.  
+</div>
+<div class="code">
+<span class="id" title="keyword">Definition</span> <a name="eqb"><span class="id" title="definition">eqb</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#addb"><span class="id" title="definition">addb</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.ssreflect.eqtype.html#b"><span class="id" title="variable">b</span></a>).<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="eqbP"><span class="id" title="lemma">eqbP</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#axiom"><span class="id" title="definition">Equality.axiom</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#eqb"><span class="id" title="definition">eqb</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Canonical</span> <span class="id" title="var">bool_eqMixin</span> := <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqMixin"><span class="id" title="abbreviation">EqMixin</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#eqbP"><span class="id" title="lemma">eqbP</span></a>.<br/>
+<span class="id" title="keyword">Canonical</span> <span class="id" title="var">bool_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#EqType"><span class="id" title="abbreviation">EqType</span></a> <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> <a class="idref" href="mathcomp.ssreflect.eqtype.html#bool_eqMixin"><span class="id" title="definition">bool_eqMixin</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="eqbE"><span class="id" title="lemma">eqbE</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#eqb"><span class="id" title="definition">eqb</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.ssreflect.eqtype.html#eq_op"><span class="id" title="definition">eq_op</span></a>.  <br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="bool_irrelevance"><span class="id" title="lemma">bool_irrelevance</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/8.8.0/stdlib//Coq.Init.Datatypes.html#bool"><span class="id" title="inductive">bool</span></a>) (<span class="id" title="var">E</span> <span class="id" title="var">E'</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.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="mathcomp.ssreflect.eqtype.html#y"><span class="id" title="variable">y</span></a>) : <a class="idref" href="mathcomp.ssreflect.eqtype.html#E"><span class="id" title="variable">E</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.ssreflect.eqtype.html#E'"><span class="id" title="variable">E'</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="negb_add"><span class="id" title="lemma">negb_add</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/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.ssreflect.eqtype.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#ef177bde7d01ae97c98f9cba81f6c95b"><span class="id" title="notation">(+)</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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#4b80c70cdb231351c5e129ba61f7f956"><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.ssreflect.eqtype.html#b1"><span class="id" title="variable">b1</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="negb_eqb"><span class="id" title="lemma">negb_eqb</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/8.8.0/stdlib//Coq.Init.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#b1"><span class="id" title="variable">b1</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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> <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.ssreflect.eqtype.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#ef177bde7d01ae97c98f9cba81f6c95b"><span class="id" title="notation">(+)</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b2"><span class="id" title="variable">b2</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="eqb_id"><span class="id" title="lemma">eqb_id</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.ssreflect.eqtype.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</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.ssreflect.eqtype.html#b"><span class="id" title="variable">b</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="eqbF_neg"><span class="id" title="lemma">eqbF_neg</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.ssreflect.eqtype.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><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.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.ssreflect.eqtype.html#b"><span class="id" title="variable">b</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="eqb_negLR"><span class="id" title="lemma">eqb_negLR</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/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.ssreflect.eqtype.html#b1"><span class="id" title="variable">b1</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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> <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.ssreflect.eqtype.html#b1"><span class="id" title="variable">b1</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><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.ssreflect.eqtype.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/>
+ 
+<br/>
+</div>
+
+<div class="doc">
+ Equality-based predicates.        
+</div>
+<div class="code">
+
+<br/>
+<span class="id" title="keyword">Notation</span> <a name="xpred1"><span class="id" title="abbreviation">xpred1</span></a> := (<span class="id" title="keyword">fun</span> <span class="id" title="var">a1</span> <span class="id" title="var">x</span> ⇒ <a class="idref" href="mathcomp.ssreflect.eqtype.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.ssreflect.eqtype.html#a1"><span class="id" title="variable">a1</span></a>).<br/>
+<span class="id" title="keyword">Notation</span> <a name="xpred2"><span class="id" title="abbreviation">xpred2</span></a> := (<span class="id" title="keyword">fun</span> <span class="id" title="var">a1</span> <span class="id" title="var">a2</span> <span class="id" title="var">x</span> ⇒ <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.ssreflect.eqtype.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.ssreflect.eqtype.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.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="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.ssreflect.eqtype.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.ssreflect.eqtype.html#a2"><span class="id" title="variable">a2</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">Notation</span> <a name="xpred3"><span class="id" title="abbreviation">xpred3</span></a> := (<span class="id" title="keyword">fun</span> <span class="id" title="var">a1</span> <span class="id" title="var">a2</span> <span class="id" title="var">a3</span> <span class="id" title="var">x</span> ⇒ <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.ssreflect.eqtype.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.ssreflect.eqtype.html#a1"><span class="id" title="variable">a1</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.ssreflect.eqtype.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.ssreflect.eqtype.html#a2"><span class="id" title="variable">a2</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.ssreflect.eqtype.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.ssreflect.eqtype.html#a3"><span class="id" title="variable">a3</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">Notation</span> <a name="xpred4"><span class="id" title="abbreviation">xpred4</span></a> :=<br/>
+&nbsp;&nbsp;(<span class="id" title="keyword">fun</span> <span class="id" title="var">a1</span> <span class="id" title="var">a2</span> <span class="id" title="var">a3</span> <span class="id" title="var">a4</span> <span class="id" title="var">x</span> ⇒ <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.ssreflect.eqtype.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.ssreflect.eqtype.html#a1"><span class="id" title="variable">a1</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.ssreflect.eqtype.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.ssreflect.eqtype.html#a2"><span class="id" title="variable">a2</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.ssreflect.eqtype.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.ssreflect.eqtype.html#a3"><span class="id" title="variable">a3</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.ssreflect.eqtype.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.ssreflect.eqtype.html#a4"><span class="id" title="variable">a4</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">Notation</span> <a name="xpredU1"><span class="id" title="abbreviation">xpredU1</span></a> := (<span class="id" title="keyword">fun</span> <span class="id" title="var">a1</span> (<span class="id" title="var">p</span> : <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> <span class="id" title="var">_</span>) <span class="id" title="var">x</span> ⇒ <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.ssreflect.eqtype.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.ssreflect.eqtype.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.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.ssreflect.eqtype.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a>).<br/>
+<span class="id" title="keyword">Notation</span> <a name="xpredC1"><span class="id" title="abbreviation">xpredC1</span></a> := (<span class="id" title="keyword">fun</span> <span class="id" title="var">a1</span> <span class="id" title="var">x</span> ⇒ <a class="idref" href="mathcomp.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#a1"><span class="id" title="variable">a1</span></a>).<br/>
+<span class="id" title="keyword">Notation</span> <a name="xpredD1"><span class="id" title="abbreviation">xpredD1</span></a> := (<span class="id" title="keyword">fun</span> (<span class="id" title="var">p</span> : <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> <span class="id" title="var">_</span>) <span class="id" title="var">a1</span> <span class="id" title="var">x</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="mathcomp.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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.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="mathcomp.ssreflect.eqtype.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a>).<br/>
+
+<br/>
+<span class="id" title="keyword">Section</span> <a name="EqPred"><span class="id" title="section">EqPred</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Variable</span> <a name="EqPred.T"><span class="id" title="variable">T</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#eqType"><span class="id" title="abbreviation">eqType</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="pred1"><span class="id" title="definition">pred1</span></a> (<span class="id" title="var">a1</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqPred.T"><span class="id" title="variable">T</span></a>) := <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#SimplPred"><span class="id" title="definition">SimplPred</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#xpred1"><span class="id" title="abbreviation">xpred1</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#a1"><span class="id" title="variable">a1</span></a>).<br/>
+<span class="id" title="keyword">Definition</span> <a name="pred2"><span class="id" title="definition">pred2</span></a> (<span class="id" title="var">a1</span> <span class="id" title="var">a2</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqPred.T"><span class="id" title="variable">T</span></a>) := <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#SimplPred"><span class="id" title="definition">SimplPred</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#xpred2"><span class="id" title="abbreviation">xpred2</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#a1"><span class="id" title="variable">a1</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#a2"><span class="id" title="variable">a2</span></a>).<br/>
+<span class="id" title="keyword">Definition</span> <a name="pred3"><span class="id" title="definition">pred3</span></a> (<span class="id" title="var">a1</span> <span class="id" title="var">a2</span> <span class="id" title="var">a3</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqPred.T"><span class="id" title="variable">T</span></a>) := <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#SimplPred"><span class="id" title="definition">SimplPred</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#xpred3"><span class="id" title="abbreviation">xpred3</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#a1"><span class="id" title="variable">a1</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#a2"><span class="id" title="variable">a2</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#a3"><span class="id" title="variable">a3</span></a>).<br/>
+<span class="id" title="keyword">Definition</span> <a name="pred4"><span class="id" title="definition">pred4</span></a> (<span class="id" title="var">a1</span> <span class="id" title="var">a2</span> <span class="id" title="var">a3</span> <span class="id" title="var">a4</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqPred.T"><span class="id" title="variable">T</span></a>) := <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#SimplPred"><span class="id" title="definition">SimplPred</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#xpred4"><span class="id" title="abbreviation">xpred4</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#a1"><span class="id" title="variable">a1</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#a2"><span class="id" title="variable">a2</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#a3"><span class="id" title="variable">a3</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#a4"><span class="id" title="variable">a4</span></a>).<br/>
+<span class="id" title="keyword">Definition</span> <a name="predU1"><span class="id" title="definition">predU1</span></a> (<span class="id" title="var">a1</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqPred.T"><span class="id" title="variable">T</span></a>) <span class="id" title="var">p</span> := <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#SimplPred"><span class="id" title="definition">SimplPred</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#xpredU1"><span class="id" title="abbreviation">xpredU1</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#a1"><span class="id" title="variable">a1</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#p"><span class="id" title="variable">p</span></a>).<br/>
+<span class="id" title="keyword">Definition</span> <a name="predC1"><span class="id" title="definition">predC1</span></a> (<span class="id" title="var">a1</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqPred.T"><span class="id" title="variable">T</span></a>) := <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#SimplPred"><span class="id" title="definition">SimplPred</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#xpredC1"><span class="id" title="abbreviation">xpredC1</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#a1"><span class="id" title="variable">a1</span></a>).<br/>
+<span class="id" title="keyword">Definition</span> <a name="predD1"><span class="id" title="definition">predD1</span></a> <span class="id" title="var">p</span> (<span class="id" title="var">a1</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqPred.T"><span class="id" title="variable">T</span></a>) := <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#SimplPred"><span class="id" title="definition">SimplPred</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#xpredD1"><span class="id" title="abbreviation">xpredD1</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#a1"><span class="id" title="variable">a1</span></a>).<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="pred1E"><span class="id" title="lemma">pred1E</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#pred1"><span class="id" title="definition">pred1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#86efabaf3ab961ac3d2bac35d2b3c35d"><span class="id" title="notation">=2</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#eq_op"><span class="id" title="definition">eq_op</span></a>.  <br/>
+
+<br/>
+<span class="id" title="keyword">Variables</span> (<a name="EqPred.T2"><span class="id" title="variable">T2</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#eqType"><span class="id" title="abbreviation">eqType</span></a>) (<a name="EqPred.x"><span class="id" title="variable">x</span></a> <a name="EqPred.y"><span class="id" title="variable">y</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqPred.T"><span class="id" title="variable">T</span></a>) (<a name="EqPred.z"><span class="id" title="variable">z</span></a> <a name="EqPred.u"><span class="id" title="variable">u</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#T2"><span class="id" title="variable">T2</span></a>) (<a name="EqPred.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#bool"><span class="id" title="inductive">bool</span></a>).<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="predU1P"><span class="id" title="lemma">predU1P</span></a> : <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.ssreflect.eqtype.html#EqPred.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="mathcomp.ssreflect.eqtype.html#EqPred.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#7a45dffb109c3069e5c675be68643e60"><span class="id" title="notation">∨</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqPred.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><a class="idref" href="mathcomp.ssreflect.eqtype.html#EqPred.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.ssreflect.eqtype.html#EqPred.y"><span class="id" title="variable">y</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="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.ssreflect.eqtype.html#EqPred.b"><span class="id" title="variable">b</span></a>).<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="pred2P"><span class="id" title="lemma">pred2P</span></a> : <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.ssreflect.eqtype.html#EqPred.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="mathcomp.ssreflect.eqtype.html#EqPred.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#7a45dffb109c3069e5c675be68643e60"><span class="id" title="notation">∨</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqPred.z"><span class="id" title="variable">z</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.ssreflect.eqtype.html#EqPred.u"><span class="id" title="variable">u</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.ssreflect.eqtype.html#EqPred.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.ssreflect.eqtype.html#EqPred.y"><span class="id" title="variable">y</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="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.ssreflect.eqtype.html#EqPred.z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqPred.u"><span class="id" title="variable">u</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/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="predD1P"><span class="id" title="lemma">predD1P</span></a> : <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.ssreflect.eqtype.html#EqPred.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#32263a1c8b01baecdff9deb038955bc9"><span class="id" title="notation">≠</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqPred.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#d82a7d96d3659d805ffe732283716822"><span class="id" title="notation">∧</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqPred.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><a class="idref" href="mathcomp.ssreflect.eqtype.html#EqPred.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqPred.y"><span class="id" title="variable">y</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="mathcomp.ssreflect.eqtype.html#EqPred.b"><span class="id" title="variable">b</span></a>).<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="predU1l"><span class="id" title="lemma">predU1l</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqPred.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="mathcomp.ssreflect.eqtype.html#EqPred.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="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.ssreflect.eqtype.html#EqPred.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.ssreflect.eqtype.html#EqPred.y"><span class="id" title="variable">y</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="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.ssreflect.eqtype.html#EqPred.b"><span class="id" title="variable">b</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="predU1r"><span class="id" title="lemma">predU1r</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqPred.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="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.ssreflect.eqtype.html#EqPred.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.ssreflect.eqtype.html#EqPred.y"><span class="id" title="variable">y</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="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.ssreflect.eqtype.html#EqPred.b"><span class="id" title="variable">b</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="eqVneq"><span class="id" title="lemma">eqVneq</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#5bf2050e90b21ebc82dc5463d1ba338e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#EqPred.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="mathcomp.ssreflect.eqtype.html#EqPred.y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#5bf2050e90b21ebc82dc5463d1ba338e"><span class="id" title="notation">}</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#5bf2050e90b21ebc82dc5463d1ba338e"><span class="id" title="notation">+</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#5bf2050e90b21ebc82dc5463d1ba338e"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#EqPred.x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b1eeadc2feabc7422252baa895418c7b"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqPred.y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#5bf2050e90b21ebc82dc5463d1ba338e"><span class="id" title="notation">}</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqPred"><span class="id" title="section">EqPred</span></a>.<br/>
+
+<br/>
+
+<br/>
+<span class="id" title="keyword">Notation</span> <a name="f83044a80bb642c2069adf1ec8907b36"><span class="id" title="notation">&quot;</span></a>[ 'predU1' x &amp; A ]" := (<a class="idref" href="mathcomp.ssreflect.eqtype.html#predU1"><span class="id" title="definition">predU1</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#913cf87021a195b218018885aad8c94f"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#913cf87021a195b218018885aad8c94f"><span class="id" title="notation">mem</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#913cf87021a195b218018885aad8c94f"><span class="id" title="notation">]</span></a>)<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> "[ 'predU1'  x  &amp;  A ]") : <span class="id" title="var">fun_scope</span>.<br/>
+<span class="id" title="keyword">Notation</span> <a name="11efb36d4e2b98f4519391785d68e99e"><span class="id" title="notation">&quot;</span></a>[ 'predD1' A &amp; x ]" := (<a class="idref" href="mathcomp.ssreflect.eqtype.html#predD1"><span class="id" title="definition">predD1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#913cf87021a195b218018885aad8c94f"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#913cf87021a195b218018885aad8c94f"><span class="id" title="notation">mem</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#913cf87021a195b218018885aad8c94f"><span class="id" title="notation">]</span></a> <span class="id" title="var">x</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> "[ 'predD1'  A  &amp;  x ]") : <span class="id" title="var">fun_scope</span>.<br/>
+
+<br/>
+</div>
+
+<div class="doc">
+ Lemmas for reflected equality and functions.    
+</div>
+<div class="code">
+
+<br/>
+<span class="id" title="keyword">Section</span> <a name="EqFun"><span class="id" title="section">EqFun</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Section</span> <a name="EqFun.Exo"><span class="id" title="section">Exo</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Variables</span> (<a name="EqFun.Exo.aT"><span class="id" title="variable">aT</span></a> <a name="EqFun.Exo.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#eqType"><span class="id" title="abbreviation">eqType</span></a>) (<a name="EqFun.Exo.D"><span class="id" title="variable">D</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.ssreflect.eqtype.html#aT"><span class="id" title="variable">aT</span></a>) (<a name="EqFun.Exo.f"><span class="id" title="variable">f</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#aT"><span class="id" title="variable">aT</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.ssreflect.eqtype.html#rT"><span class="id" title="variable">rT</span></a>) (<a name="EqFun.Exo.g"><span class="id" title="variable">g</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#rT"><span class="id" title="variable">rT</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.ssreflect.eqtype.html#aT"><span class="id" title="variable">aT</span></a>).<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="inj_eq"><span class="id" title="lemma">inj_eq</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.Exo.f"><span class="id" title="variable">f</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> <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> <span class="id" title="var">y</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.ssreflect.eqtype.html#EqFun.Exo.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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.ssreflect.eqtype.html#EqFun.Exo.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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> <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.ssreflect.eqtype.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.ssreflect.eqtype.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="can_eq"><span class="id" title="lemma">can_eq</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#cancel"><span class="id" title="definition">cancel</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.Exo.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.Exo.g"><span class="id" title="variable">g</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> <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> <span class="id" title="var">y</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.ssreflect.eqtype.html#EqFun.Exo.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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.ssreflect.eqtype.html#EqFun.Exo.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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> <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.ssreflect.eqtype.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.ssreflect.eqtype.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="bij_eq"><span class="id" title="lemma">bij_eq</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#bijective"><span class="id" title="inductive">bijective</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.Exo.f"><span class="id" title="variable">f</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> <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> <span class="id" title="var">y</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.ssreflect.eqtype.html#EqFun.Exo.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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.ssreflect.eqtype.html#EqFun.Exo.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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> <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.ssreflect.eqtype.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.ssreflect.eqtype.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="can2_eq"><span class="id" title="lemma">can2_eq</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#cancel"><span class="id" title="definition">cancel</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.Exo.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.Exo.g"><span class="id" title="variable">g</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.ssrfun.html#cancel"><span class="id" title="definition">cancel</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.Exo.g"><span class="id" title="variable">g</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.Exo.f"><span class="id" title="variable">f</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> <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> <span class="id" title="var">y</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.ssreflect.eqtype.html#EqFun.Exo.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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.ssreflect.eqtype.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> <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.ssreflect.eqtype.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.ssreflect.eqtype.html#EqFun.Exo.g"><span class="id" title="variable">g</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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="inj_in_eq"><span class="id" title="lemma">inj_in_eq</span></a> :<br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.Exo.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">&amp;,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.Exo.f"><span class="id" title="variable">f</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><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#2bba53854f326a714d377124cccec593"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.Exo.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">&amp;,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> <span class="id" title="var">y</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.ssreflect.eqtype.html#EqFun.Exo.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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.ssreflect.eqtype.html#EqFun.Exo.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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> <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.ssreflect.eqtype.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.ssreflect.eqtype.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><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">}</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="can_in_eq"><span class="id" title="lemma">can_in_eq</span></a> :<br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.Exo.D"><span class="id" title="variable">D</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#cancel"><span class="id" title="definition">cancel</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.Exo.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.Exo.g"><span class="id" title="variable">g</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><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#2bba53854f326a714d377124cccec593"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.Exo.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">&amp;,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> <span class="id" title="var">y</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.ssreflect.eqtype.html#EqFun.Exo.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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.ssreflect.eqtype.html#EqFun.Exo.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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> <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.ssreflect.eqtype.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.ssreflect.eqtype.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><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#2bba53854f326a714d377124cccec593"><span class="id" title="notation">}</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.Exo"><span class="id" title="section">Exo</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Section</span> <a name="EqFun.Endo"><span class="id" title="section">Endo</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Variable</span> <a name="EqFun.Endo.T"><span class="id" title="variable">T</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#eqType"><span class="id" title="abbreviation">eqType</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="frel"><span class="id" title="definition">frel</span></a> <span class="id" title="var">f</span> := <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#a3fa885266d530b93c1b9f67891df8e8"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#a3fa885266d530b93c1b9f67891df8e8"><span class="id" title="notation">rel</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/8.8.0/stdlib//Coq.ssr.ssrbool.html#a3fa885266d530b93c1b9f67891df8e8"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.Endo.T"><span class="id" title="variable">T</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#a3fa885266d530b93c1b9f67891df8e8"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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.ssreflect.eqtype.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#a3fa885266d530b93c1b9f67891df8e8"><span class="id" title="notation">]</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="inv_eq"><span class="id" title="lemma">inv_eq</span></a> <span class="id" title="var">f</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#involutive"><span class="id" title="definition">involutive</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#f"><span class="id" title="variable">f</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> <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.Endo.T"><span class="id" title="variable">T</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.ssreflect.eqtype.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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.ssreflect.eqtype.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> <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.ssreflect.eqtype.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.ssreflect.eqtype.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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="eq_frel"><span class="id" title="lemma">eq_frel</span></a> <span class="id" title="var">f</span> <span class="id" title="var">f'</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#2500d48ed8e862ccfda98a44dff88963"><span class="id" title="notation">=1</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#f'"><span class="id" title="variable">f'</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.ssreflect.eqtype.html#frel"><span class="id" title="definition">frel</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#86efabaf3ab961ac3d2bac35d2b3c35d"><span class="id" title="notation">=2</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#frel"><span class="id" title="definition">frel</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#f'"><span class="id" title="variable">f'</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.Endo"><span class="id" title="section">Endo</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Variable</span> <a name="EqFun.aT"><span class="id" title="variable">aT</span></a> : <span class="id" title="keyword">Type</span>.<br/>
+
+<br/>
+</div>
+
+<div class="doc">
+ The invariant of an function f wrt a projection k is the pred of points 
+ that have the same projection as their image.                            
+</div>
+<div class="code">
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="invariant"><span class="id" title="definition">invariant</span></a> (<span class="id" title="var">rT</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#eqType"><span class="id" title="abbreviation">eqType</span></a>) <span class="id" title="var">f</span> (<span class="id" title="var">k</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.aT"><span class="id" title="variable">aT</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.ssreflect.eqtype.html#rT"><span class="id" title="variable">rT</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> <a class="idref" href="mathcomp.ssreflect.eqtype.html#k"><span class="id" title="variable">k</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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.ssreflect.eqtype.html#k"><span class="id" title="variable">k</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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#880a9790dece461a678db8aa0c091f63"><span class="id" title="notation">]</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Variables</span> (<a name="EqFun.rT1"><span class="id" title="variable">rT1</span></a> <a name="EqFun.rT2"><span class="id" title="variable">rT2</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#eqType"><span class="id" title="abbreviation">eqType</span></a>) (<a name="EqFun.f"><span class="id" title="variable">f</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.aT"><span class="id" title="variable">aT</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.ssreflect.eqtype.html#EqFun.aT"><span class="id" title="variable">aT</span></a>) (<a name="EqFun.h"><span class="id" title="variable">h</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#rT1"><span class="id" title="variable">rT1</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.ssreflect.eqtype.html#rT2"><span class="id" title="variable">rT2</span></a>) (<a name="EqFun.k"><span class="id" title="variable">k</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.aT"><span class="id" title="variable">aT</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.ssreflect.eqtype.html#rT1"><span class="id" title="variable">rT1</span></a>).<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="invariant_comp"><span class="id" title="lemma">invariant_comp</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#subpred"><span class="id" title="definition">subpred</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#invariant"><span class="id" title="definition">invariant</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.k"><span class="id" title="variable">k</span></a>) (<a class="idref" href="mathcomp.ssreflect.eqtype.html#invariant"><span class="id" title="definition">invariant</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.f"><span class="id" title="variable">f</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.h"><span class="id" title="variable">h</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#1b4394c5c1740ef3dc9e4224084970bb"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#1b4394c5c1740ef3dc9e4224084970bb"><span class="id" title="notation">o</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.k"><span class="id" title="variable">k</span></a>)).<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="invariant_inj"><span class="id" title="lemma">invariant_inj</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.h"><span class="id" title="variable">h</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.ssreflect.eqtype.html#invariant"><span class="id" title="definition">invariant</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.f"><span class="id" title="variable">f</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.h"><span class="id" title="variable">h</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#1b4394c5c1740ef3dc9e4224084970bb"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#1b4394c5c1740ef3dc9e4224084970bb"><span class="id" title="notation">o</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.k"><span class="id" title="variable">k</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#2500d48ed8e862ccfda98a44dff88963"><span class="id" title="notation">=1</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#invariant"><span class="id" title="definition">invariant</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun.k"><span class="id" title="variable">k</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqFun"><span class="id" title="section">EqFun</span></a>.<br/>
+
+<br/>
+
+<br/>
+</div>
+
+<div class="doc">
+ The coercion to rel must be explicit for derived Notations to unparse.  
+</div>
+<div class="code">
+<span class="id" title="keyword">Notation</span> <a name="coerced_frel"><span class="id" title="abbreviation">coerced_frel</span></a> <span class="id" title="var">f</span> := (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#rel_of_simpl_rel"><span class="id" title="definition">rel_of_simpl_rel</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#frel"><span class="id" title="definition">frel</span></a> <span class="id" title="var">f</span>)) (<span class="id" title="var">only</span> <span class="id" title="var">parsing</span>).<br/>
+
+<br/>
+<span class="id" title="keyword">Section</span> <a name="FunWith"><span class="id" title="section">FunWith</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Variables</span> (<a name="FunWith.aT"><span class="id" title="variable">aT</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#eqType"><span class="id" title="abbreviation">eqType</span></a>) (<a name="FunWith.rT"><span class="id" title="variable">rT</span></a> : <span class="id" title="keyword">Type</span>).<br/>
+
+<br/>
+<span class="id" title="keyword">CoInductive</span> <a name="fun_delta"><span class="id" title="inductive">fun_delta</span></a> : <span class="id" title="keyword">Type</span> := <a name="FunDelta"><span class="id" title="constructor">FunDelta</span></a> <span class="id" title="keyword">of</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#FunWith.aT"><span class="id" title="variable">aT</span></a> &amp; <a class="idref" href="mathcomp.ssreflect.eqtype.html#FunWith.rT"><span class="id" title="variable">rT</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="fwith"><span class="id" title="definition">fwith</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> (<span class="id" title="var">f</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#FunWith.aT"><span class="id" title="variable">aT</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.ssreflect.eqtype.html#FunWith.rT"><span class="id" title="variable">rT</span></a>) := <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#0bba0687209e799f52ace6d4b2c6d64a"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#0bba0687209e799f52ace6d4b2c6d64a"><span class="id" title="notation">fun</span></a> <span class="id" title="var">z</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#0bba0687209e799f52ace6d4b2c6d64a"><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">if</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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">then</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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.ssreflect.eqtype.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#z"><span class="id" title="variable">z</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#0bba0687209e799f52ace6d4b2c6d64a"><span class="id" title="notation">]</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="app_fdelta"><span class="id" title="definition">app_fdelta</span></a> <span class="id" title="var">df</span> <span class="id" title="var">f</span> <span class="id" title="var">z</span> :=<br/>
+&nbsp;&nbsp;<span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.ssreflect.eqtype.html#FunDelta"><span class="id" title="constructor">FunDelta</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> := <a class="idref" href="mathcomp.ssreflect.eqtype.html#df"><span class="id" title="variable">df</span></a> <span class="id" title="tactic">in</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.ssreflect.eqtype.html#z"><span class="id" title="variable">z</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <span class="id" title="var">x</span> <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> <span class="id" title="var">y</span> <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.ssreflect.eqtype.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#z"><span class="id" title="variable">z</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#FunWith"><span class="id" title="section">FunWith</span></a>.<br/>
+
+<br/>
+
+<br/>
+<span class="id" title="keyword">Notation</span> <a name="208083cddfca3726231c4e84b7c928c1"><span class="id" title="notation">&quot;</span></a>x |-&gt; y" := (<a class="idref" href="mathcomp.ssreflect.eqtype.html#FunDelta"><span class="id" title="constructor">FunDelta</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span>)<br/>
+&nbsp;&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 190, <span class="id" title="keyword">no</span> <span class="id" title="keyword">associativity</span>,<br/>
+&nbsp;&nbsp;&nbsp;<span class="id" title="var">format</span> "'[hv' x '/ '  |-&gt;  y ']'") : <span class="id" title="var">fun_delta_scope</span>.<br/>
+
+<br/>
+<span class="id" title="keyword">Delimit</span> <span class="id" title="keyword">Scope</span> <span class="id" title="var">fun_delta_scope</span> <span class="id" title="keyword">with</span> <span class="id" title="var">FUN_DELTA</span>.<br/>
+
+<br/>
+<span class="id" title="keyword">Notation</span> <a name="5abbab48320225f661205a8ff4b0991d"><span class="id" title="notation">&quot;</span></a>[ 'fun' z : T =&gt; F 'with' d1 , .. , dn ]" :=<br/>
+&nbsp;&nbsp;(<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#SimplFunDelta"><span class="id" title="definition">SimplFunDelta</span></a> (<span class="id" title="keyword">fun</span> <span class="id" title="var">z</span> : <span class="id" title="var">T</span> ⇒<br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="mathcomp.ssreflect.eqtype.html#app_fdelta"><span class="id" title="definition">app_fdelta</span></a> <span class="id" title="var">d1</span>%<span class="id" title="var">FUN_DELTA</span> .. (<a class="idref" href="mathcomp.ssreflect.eqtype.html#app_fdelta"><span class="id" title="definition">app_fdelta</span></a> <span class="id" title="var">dn</span>%<span class="id" title="var">FUN_DELTA</span>  (<span class="id" title="keyword">fun</span> <span class="id" title="var">_</span> ⇒ <span class="id" title="var">F</span>)) ..))<br/>
+&nbsp;&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">z</span> <span class="id" title="var">ident</span>, <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">fun_scope</span>.<br/>
+
+<br/>
+<span class="id" title="keyword">Notation</span> <a name="98daeff9b38ed89b3ac0db77b4ceb901"><span class="id" title="notation">&quot;</span></a>[ 'fun' z =&gt; F 'with' d1 , .. , dn ]" :=<br/>
+&nbsp;&nbsp;(<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#SimplFunDelta"><span class="id" title="definition">SimplFunDelta</span></a> (<span class="id" title="keyword">fun</span> <span class="id" title="var">z</span> ⇒<br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="mathcomp.ssreflect.eqtype.html#app_fdelta"><span class="id" title="definition">app_fdelta</span></a> <span class="id" title="var">d1</span>%<span class="id" title="var">FUN_DELTA</span> .. (<a class="idref" href="mathcomp.ssreflect.eqtype.html#app_fdelta"><span class="id" title="definition">app_fdelta</span></a> <span class="id" title="var">dn</span>%<span class="id" title="var">FUN_DELTA</span> (<span class="id" title="keyword">fun</span> <span class="id" title="var">_</span> ⇒ <span class="id" title="var">F</span>)) ..))<br/>
+&nbsp;&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">z</span> <span class="id" title="var">ident</span>, <span class="id" title="var">format</span><br/>
+&nbsp;&nbsp;&nbsp;"'[hv' [ '[' 'fun'  z  =&gt; '/ '  F ']' '/'  'with'  '[' d1 , '/'  .. , '/'  dn ']' ] ']'"<br/>
+&nbsp;&nbsp;&nbsp;) : <span class="id" title="var">fun_scope</span>.<br/>
+
+<br/>
+<span class="id" title="keyword">Notation</span> <a name="567afa6fb1db7dcd21b2a36fff7bcf36"><span class="id" title="notation">&quot;</span></a>[ 'eta' f 'with' d1 , .. , dn ]" :=<br/>
+&nbsp;&nbsp;(<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#SimplFunDelta"><span class="id" title="definition">SimplFunDelta</span></a> (<span class="id" title="keyword">fun</span> <span class="id" title="var">_</span> ⇒<br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="mathcomp.ssreflect.eqtype.html#app_fdelta"><span class="id" title="definition">app_fdelta</span></a> <span class="id" title="var">d1</span>%<span class="id" title="var">FUN_DELTA</span> .. (<a class="idref" href="mathcomp.ssreflect.eqtype.html#app_fdelta"><span class="id" title="definition">app_fdelta</span></a> <span class="id" title="var">dn</span>%<span class="id" title="var">FUN_DELTA</span> <span class="id" title="var">f</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><br/>
+&nbsp;&nbsp;"'[hv' [ '[' 'eta' '/ '  f ']' '/'  'with'  '[' d1 , '/'  .. , '/'  dn ']' ] ']'"<br/>
+&nbsp;&nbsp;) : <span class="id" title="var">fun_scope</span>.<br/>
+
+<br/>
+</div>
+
+<div class="doc">
+ Various EqType constructions.                                          
+</div>
+<div class="code">
+
+<br/>
+<span class="id" title="keyword">Section</span> <a name="ComparableType"><span class="id" title="section">ComparableType</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Variable</span> <a name="ComparableType.T"><span class="id" title="variable">T</span></a> : <span class="id" title="keyword">Type</span>.<br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="comparable"><span class="id" title="definition">comparable</span></a> := <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#ComparableType.T"><span class="id" title="variable">T</span></a>, <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#decidable"><span class="id" title="definition">decidable</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.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="mathcomp.ssreflect.eqtype.html#y"><span class="id" title="variable">y</span></a>).<br/>
+
+<br/>
+<span class="id" title="keyword">Hypothesis</span> <a name="ComparableType.Hcompare"><span class="id" title="variable">Hcompare</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#comparable"><span class="id" title="definition">comparable</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="compareb"><span class="id" title="definition">compareb</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/8.8.0/stdlib//Coq.Init.Datatypes.html#bool"><span class="id" title="inductive">bool</span></a> := <a class="idref" href="mathcomp.ssreflect.eqtype.html#ComparableType.Hcompare"><span class="id" title="variable">Hcompare</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#y"><span class="id" title="variable">y</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="compareP"><span class="id" title="lemma">compareP</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#axiom"><span class="id" title="definition">Equality.axiom</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#compareb"><span class="id" title="definition">compareb</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="comparableClass"><span class="id" title="definition">comparableClass</span></a> := <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqMixin"><span class="id" title="abbreviation">EqMixin</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#compareP"><span class="id" title="lemma">compareP</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#ComparableType"><span class="id" title="section">ComparableType</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="eq_comparable"><span class="id" title="definition">eq_comparable</span></a> (<span class="id" title="var">T</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#eqType"><span class="id" title="abbreviation">eqType</span></a>) : <a class="idref" href="mathcomp.ssreflect.eqtype.html#comparable"><span class="id" title="definition">comparable</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#T"><span class="id" title="variable">T</span></a> :=<br/>
+&nbsp;&nbsp;<span class="id" title="keyword">fun</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#decP"><span class="id" title="definition">decP</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#ab7a7bc39754581ab8f205db64711d57"><span class="id" title="notation">=</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#ab7a7bc39754581ab8f205db64711d57"><span class="id" title="notation">P</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#y"><span class="id" title="variable">y</span></a>).<br/>
+
+<br/>
+<span class="id" title="keyword">Section</span> <a name="SubType"><span class="id" title="section">SubType</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Variables</span> (<a name="SubType.T"><span class="id" title="variable">T</span></a> : <span class="id" title="keyword">Type</span>) (<a name="SubType.P"><span class="id" title="variable">P</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.ssreflect.eqtype.html#T"><span class="id" title="variable">T</span></a>).<br/>
+
+<br/>
+<span class="id" title="keyword">Structure</span> <a name="subType"><span class="id" title="record">subType</span></a> : <span class="id" title="keyword">Type</span> := <a name="SubType"><span class="id" title="constructor">SubType</span></a> {<br/>
+&nbsp;&nbsp;<a name="sub_sort"><span class="id" title="projection">sub_sort</span></a> :&gt; <span class="id" title="keyword">Type</span>;<br/>
+&nbsp;&nbsp;<a name="val"><span class="id" title="projection">val</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#sub_sort"><span class="id" title="method">sub_sort</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.ssreflect.eqtype.html#SubType.T"><span class="id" title="variable">T</span></a>;<br/>
+&nbsp;&nbsp;<a name="Sub"><span class="id" title="projection">Sub</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span>, <a class="idref" href="mathcomp.ssreflect.eqtype.html#SubType.P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#sub_sort"><span class="id" title="method">sub_sort</span></a>;<br/>
+&nbsp;&nbsp;<span class="id" title="var">_</span> : <span class="id" title="keyword">∀</span> <span class="id" title="var">K</span> (<span class="id" title="var">_</span> : <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> <span class="id" title="var">Px</span>, <a class="idref" href="mathcomp.ssreflect.eqtype.html#K"><span class="id" title="variable">K</span></a> (@<a class="idref" href="mathcomp.ssreflect.eqtype.html#Sub"><span class="id" title="method">Sub</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#Px"><span class="id" title="variable">Px</span></a>)) <span class="id" title="var">u</span>, <a class="idref" href="mathcomp.ssreflect.eqtype.html#K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#u"><span class="id" title="variable">u</span></a>;<br/>
+&nbsp;&nbsp;<span class="id" title="var">_</span> : <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> <span class="id" title="var">Px</span>, <a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="method">val</span></a> (@<a class="idref" href="mathcomp.ssreflect.eqtype.html#Sub"><span class="id" title="method">Sub</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#Px"><span class="id" title="variable">Px</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.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a><br/>
+}.<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="vrefl"><span class="id" title="lemma">vrefl</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span>, <a class="idref" href="mathcomp.ssreflect.eqtype.html#SubType.P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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="mathcomp.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a>.  <br/>
+<span class="id" title="keyword">Definition</span> <a name="vrefl_rect"><span class="id" title="definition">vrefl_rect</span></a> := <a class="idref" href="mathcomp.ssreflect.eqtype.html#vrefl"><span class="id" title="lemma">vrefl</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="clone_subType"><span class="id" title="definition">clone_subType</span></a> <span class="id" title="var">U</span> <span class="id" title="var">v</span> :=<br/>
+&nbsp;&nbsp;<span class="id" title="keyword">fun</span> <span class="id" title="var">sT</span> &amp; <a class="idref" href="mathcomp.ssreflect.eqtype.html#sub_sort"><span class="id" title="projection">sub_sort</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#sT"><span class="id" title="variable">sT</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.ssreflect.eqtype.html#U"><span class="id" title="variable">U</span></a> ⇒<br/>
+&nbsp;&nbsp;<span class="id" title="keyword">fun</span> <span class="id" title="var">c</span> <span class="id" title="var">Urec</span> <span class="id" title="var">cK</span> (<span class="id" title="var">sT'</span> := @<a class="idref" href="mathcomp.ssreflect.eqtype.html#SubType"><span class="id" title="constructor">SubType</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#U"><span class="id" title="variable">U</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#v"><span class="id" title="variable">v</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c"><span class="id" title="variable">c</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#Urec"><span class="id" title="variable">Urec</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#cK"><span class="id" title="variable">cK</span></a>) &amp; <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#phant_id"><span class="id" title="definition">phant_id</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#sT'"><span class="id" title="variable">sT'</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#sT"><span class="id" title="variable">sT</span></a> ⇒ <a class="idref" href="mathcomp.ssreflect.eqtype.html#sT'"><span class="id" title="variable">sT'</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Variable</span> <a name="SubType.sT"><span class="id" title="variable">sT</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#subType"><span class="id" title="record">subType</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">CoInductive</span> <a name="Sub_spec"><span class="id" title="inductive">Sub_spec</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#SubType.sT"><span class="id" title="variable">sT</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> <span class="id" title="keyword">Type</span> := <a name="SubSpec"><span class="id" title="constructor">SubSpec</span></a> <span class="id" title="var">x</span> <span class="id" title="var">Px</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#Sub_spec"><span class="id" title="inductive">Sub_spec</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#Sub"><span class="id" title="projection">Sub</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#Px"><span class="id" title="variable">Px</span></a>).<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="SubP"><span class="id" title="lemma">SubP</span></a> <span class="id" title="var">u</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#Sub_spec"><span class="id" title="inductive">Sub_spec</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#u"><span class="id" title="variable">u</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="SubK"><span class="id" title="lemma">SubK</span></a> <span class="id" title="var">x</span> <span class="id" title="var">Px</span> : @<a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#SubType.sT"><span class="id" title="variable">sT</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#Sub"><span class="id" title="projection">Sub</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#Px"><span class="id" title="variable">Px</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.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="insub"><span class="id" title="definition">insub</span></a> <span class="id" title="var">x</span> :=<br/>
+&nbsp;&nbsp;<span class="id" title="keyword">if</span> @<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#idP"><span class="id" title="lemma">idP</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#SubType.P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a>) <span class="id" title="keyword">is</span> <span class="id" title="var">ReflectT</span> <span class="id" title="var">Px</span> <span class="id" title="keyword">then</span> @<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#Some"><span class="id" title="constructor">Some</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#SubType.sT"><span class="id" title="variable">sT</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#Sub"><span class="id" title="projection">Sub</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a> <span class="id" title="var">Px</span>) <span class="id" title="keyword">else</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#None"><span class="id" title="constructor">None</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="insubd"><span class="id" title="definition">insubd</span></a> <span class="id" title="var">u0</span> <span class="id" title="var">x</span> := <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#odflt"><span class="id" title="abbreviation">odflt</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#u0"><span class="id" title="variable">u0</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#insub"><span class="id" title="definition">insub</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a>).<br/>
+
+<br/>
+<span class="id" title="keyword">CoInductive</span> <a name="insub_spec"><span class="id" title="inductive">insub_spec</span></a> <span class="id" title="var">x</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#option"><span class="id" title="inductive">option</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#SubType.sT"><span class="id" title="variable">sT</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> <span class="id" title="keyword">Type</span> :=<br/>
+&nbsp;&nbsp;| <a name="InsubSome"><span class="id" title="constructor">InsubSome</span></a> <span class="id" title="var">u</span> <span class="id" title="keyword">of</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#SubType.P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a> &amp; <a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#u"><span class="id" title="variable">u</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.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#insub_spec"><span class="id" title="inductive">insub_spec</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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#Some"><span class="id" title="constructor">Some</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#u"><span class="id" title="variable">u</span></a>)<br/>
+&nbsp;&nbsp;| <a name="InsubNone"><span class="id" title="constructor">InsubNone</span></a>   <span class="id" title="keyword">of</span> <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.ssreflect.eqtype.html#SubType.P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a>          : <a class="idref" href="mathcomp.ssreflect.eqtype.html#insub_spec"><span class="id" title="inductive">insub_spec</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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#None"><span class="id" title="constructor">None</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="insubP"><span class="id" title="lemma">insubP</span></a> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#insub_spec"><span class="id" title="inductive">insub_spec</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#insub"><span class="id" title="definition">insub</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a>).<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="insubT"><span class="id" title="lemma">insubT</span></a> <span class="id" title="var">x</span> <span class="id" title="var">Px</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#insub"><span class="id" title="definition">insub</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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#Some"><span class="id" title="constructor">Some</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#Sub"><span class="id" title="projection">Sub</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#Px"><span class="id" title="variable">Px</span></a>).<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="insubF"><span class="id" title="lemma">insubF</span></a> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#SubType.P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#insub"><span class="id" title="definition">insub</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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#None"><span class="id" title="constructor">None</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="insubN"><span class="id" title="lemma">insubN</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#4b80c70cdb231351c5e129ba61f7f956"><span class="id" title="notation">~~</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#SubType.P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#insub"><span class="id" title="definition">insub</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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#None"><span class="id" title="constructor">None</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="isSome_insub"><span class="id" title="lemma">isSome_insub</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#2500d48ed8e862ccfda98a44dff88963"><span class="id" title="notation">(</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3f6d75f5a9cb81b61e8423a7aac22056"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3f6d75f5a9cb81b61e8423a7aac22056"><span class="id" title="notation">eta</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#insub"><span class="id" title="definition">insub</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3f6d75f5a9cb81b61e8423a7aac22056"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#4509b22bf26e3d6d771897e22bd8bc8f"><span class="id" title="notation">:</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.ssreflect.eqtype.html#SubType.T"><span class="id" title="variable">T</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#2500d48ed8e862ccfda98a44dff88963"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#2500d48ed8e862ccfda98a44dff88963"><span class="id" title="notation">=1</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#SubType.P"><span class="id" title="variable">P</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="insubK"><span class="id" title="lemma">insubK</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#ocancel"><span class="id" title="definition">ocancel</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#insub"><span class="id" title="definition">insub</span></a> (@<a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <span class="id" title="var">_</span>).<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="valP"><span class="id" title="lemma">valP</span></a> (<span class="id" title="var">u</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#SubType.sT"><span class="id" title="variable">sT</span></a>) : <a class="idref" href="mathcomp.ssreflect.eqtype.html#SubType.P"><span class="id" title="variable">P</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#u"><span class="id" title="variable">u</span></a>).<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="valK"><span class="id" title="lemma">valK</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#pcancel"><span class="id" title="definition">pcancel</span></a> (@<a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <span class="id" title="var">_</span>) <a class="idref" href="mathcomp.ssreflect.eqtype.html#insub"><span class="id" title="definition">insub</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="val_inj"><span class="id" title="lemma">val_inj</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> (@<a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#SubType.sT"><span class="id" title="variable">sT</span></a>).<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="valKd"><span class="id" title="lemma">valKd</span></a> <span class="id" title="var">u0</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#cancel"><span class="id" title="definition">cancel</span></a> (@<a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <span class="id" title="var">_</span>) (<a class="idref" href="mathcomp.ssreflect.eqtype.html#insubd"><span class="id" title="definition">insubd</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#u0"><span class="id" title="variable">u0</span></a>).<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="val_insubd"><span class="id" title="lemma">val_insubd</span></a> <span class="id" title="var">u0</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#insubd"><span class="id" title="definition">insubd</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#u0"><span class="id" title="variable">u0</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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.ssr.ssreflect.html#0348819abaa88c2cd747e8fa60dde7ae"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#SubType.P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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">then</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#u0"><span class="id" title="variable">u0</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="insubdK"><span class="id" title="lemma">insubdK</span></a> <span class="id" title="var">u0</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#SubType.P"><span class="id" title="variable">P</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#cancel"><span class="id" title="definition">cancel</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#insubd"><span class="id" title="definition">insubd</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#u0"><span class="id" title="variable">u0</span></a>) (@<a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <span class="id" title="var">_</span>)<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#5c59b35a0b51db520cf1fba473ecf127"><span class="id" title="notation">}</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="insub_eq"><span class="id" title="definition">insub_eq</span></a> <span class="id" title="var">x</span> :=<br/>
+&nbsp;&nbsp;<span class="id" title="keyword">let</span> <span class="id" title="var">Some_sub</span> <span class="id" title="var">Px</span> := <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#Some"><span class="id" title="constructor">Some</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#Sub"><span class="id" title="projection">Sub</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#Px"><span class="id" title="variable">Px</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#4509b22bf26e3d6d771897e22bd8bc8f"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#SubType.sT"><span class="id" title="variable">sT</span></a>) <span class="id" title="tactic">in</span><br/>
+&nbsp;&nbsp;<span class="id" title="keyword">let</span> <span class="id" title="var">None_sub</span> <span class="id" title="var">_</span> := <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#None"><span class="id" title="constructor">None</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.ssr.ssreflect.html#f2de61384776e923a9c502554d1079cb"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#SubType.P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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#f2de61384776e923a9c502554d1079cb"><span class="id" title="notation">as</span></a> <span class="id" title="var">Px</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#f2de61384776e923a9c502554d1079cb"><span class="id" title="notation">return</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#SubType.P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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="mathcomp.ssreflect.eqtype.html#Px"><span class="id" title="variable">Px</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> <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#f2de61384776e923a9c502554d1079cb"><span class="id" title="notation">then</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#Some_sub"><span class="id" title="variable">Some_sub</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#f2de61384776e923a9c502554d1079cb"><span class="id" title="notation">else</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#None_sub"><span class="id" title="variable">None_sub</span></a>) (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#erefl"><span class="id" title="abbreviation">erefl</span></a> <span class="id" title="var">_</span>).<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="insub_eqE"><span class="id" title="lemma">insub_eqE</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#insub_eq"><span class="id" title="definition">insub_eq</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#2500d48ed8e862ccfda98a44dff88963"><span class="id" title="notation">=1</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#insub"><span class="id" title="definition">insub</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#SubType"><span class="id" title="section">SubType</span></a>.<br/>
+
+<br/>
+
+<br/>
+
+<br/>
+
+<br/>
+<span class="id" title="keyword">Notation</span> <a name="341c160c3e7b20d967b85d1852a7f89f"><span class="id" title="notation">&quot;</span></a>[ 'subType' 'for' v ]" := (<a class="idref" href="mathcomp.ssreflect.eqtype.html#SubType"><span class="id" title="constructor">SubType</span></a> <span class="id" title="var">_</span> <span class="id" title="var">v</span> <span class="id" title="var">_</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#inlined_sub_rect"><span class="id" title="abbreviation">inlined_sub_rect</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#vrefl_rect"><span class="id" title="definition">vrefl_rect</span></a>)<br/>
+&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">form_scope</span>.<br/>
+
+<br/>
+<span class="id" title="keyword">Notation</span> <a name="415aba177721bceee8ec785947f9342f"><span class="id" title="notation">&quot;</span></a>[ 'sub' 'Type' 'for' v ]" := (<a class="idref" href="mathcomp.ssreflect.eqtype.html#SubType"><span class="id" title="constructor">SubType</span></a> <span class="id" title="var">_</span> <span class="id" title="var">v</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#vrefl_rect"><span class="id" title="definition">vrefl_rect</span></a>)<br/>
+&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "[ 'sub' 'Type'  'for'  v ]") : <span class="id" title="var">form_scope</span>.<br/>
+
+<br/>
+<span class="id" title="keyword">Notation</span> <a name="bdefe280518135f830e003d53014dbda"><span class="id" title="notation">&quot;</span></a>[ 'subType' 'for' v 'by' rec ]" := (<a class="idref" href="mathcomp.ssreflect.eqtype.html#SubType"><span class="id" title="constructor">SubType</span></a> <span class="id" title="var">_</span> <span class="id" title="var">v</span> <span class="id" title="var">_</span> <span class="id" title="keyword">rec</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#vrefl"><span class="id" title="lemma">vrefl</span></a>)<br/>
+&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "[ 'subType'  'for'  v  'by'  rec ]") : <span class="id" title="var">form_scope</span>.<br/>
+
+<br/>
+<span class="id" title="keyword">Notation</span> <a name="5a1a3176d1f13512b7b2c6b5bfb86f20"><span class="id" title="notation">&quot;</span></a>[ 'subType' 'of' U 'for' v ]" := (<a class="idref" href="mathcomp.ssreflect.eqtype.html#clone_subType"><span class="id" title="definition">clone_subType</span></a> <span class="id" title="var">U</span> <span class="id" title="var">v</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#idfun"><span class="id" title="abbreviation">idfun</span></a>)<br/>
+&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "[ 'subType'  'of'  U  'for'  v ]") : <span class="id" title="var">form_scope</span>.<br/>
+
+<br/>
+</div>
+
+<div class="doc">
+
+<div class="paragraph"> </div>
+
+Notation " [ 'subType' 'for' v ]" := (clone_subType _ v id idfun)
+ (at level 0, format " [ 'subType'  'for'  v ]") : form_scope.
+ 
+</div>
+<div class="code">
+<span class="id" title="keyword">Notation</span> <a name="6645671e2203a23d135a621a3cf0157c"><span class="id" title="notation">&quot;</span></a>[ 'subType' 'of' U ]" := (<a class="idref" href="mathcomp.ssreflect.eqtype.html#clone_subType"><span class="id" title="definition">clone_subType</span></a> <span class="id" title="var">U</span> <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a>)<br/>
+&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "[ 'subType'  'of'  U ]") : <span class="id" title="var">form_scope</span>.<br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="NewType"><span class="id" title="definition">NewType</span></a> <span class="id" title="var">T</span> <span class="id" title="var">U</span> <span class="id" title="var">v</span> <span class="id" title="var">c</span> <span class="id" title="var">Urec</span> :=<br/>
+&nbsp;&nbsp;<span class="id" title="keyword">let</span> <span class="id" title="var">Urec'</span> <span class="id" title="var">P</span> <span class="id" title="var">IH</span> := <a class="idref" href="mathcomp.ssreflect.eqtype.html#Urec"><span class="id" title="variable">Urec</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#P"><span class="id" title="variable">P</span></a> (<span class="id" title="keyword">fun</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#T"><span class="id" title="variable">T</span></a> ⇒ <a class="idref" href="mathcomp.ssreflect.eqtype.html#IH"><span class="id" title="variable">IH</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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#isT"><span class="id" title="definition">isT</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#4509b22bf26e3d6d771897e22bd8bc8f"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#P"><span class="id" title="variable">P</span></a> <span class="id" title="var">_</span>) <span class="id" title="tactic">in</span><br/>
+&nbsp;&nbsp;<a class="idref" href="mathcomp.ssreflect.eqtype.html#SubType"><span class="id" title="constructor">SubType</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#U"><span class="id" title="variable">U</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#v"><span class="id" title="variable">v</span></a> (<span class="id" title="keyword">fun</span> <span class="id" title="var">x</span> <span class="id" title="var">_</span> ⇒ <a class="idref" href="mathcomp.ssreflect.eqtype.html#c"><span class="id" title="variable">c</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a>) <a class="idref" href="mathcomp.ssreflect.eqtype.html#Urec'"><span class="id" title="variable">Urec'</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Notation</span> <a name="d716e206e5129c6b3a60f0f640eaaeb0"><span class="id" title="notation">&quot;</span></a>[ 'newType' 'for' v ]" := (<a class="idref" href="mathcomp.ssreflect.eqtype.html#NewType"><span class="id" title="definition">NewType</span></a> <span class="id" title="var">v</span> <span class="id" title="var">_</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#inlined_new_rect"><span class="id" title="abbreviation">inlined_new_rect</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#vrefl_rect"><span class="id" title="definition">vrefl_rect</span></a>)<br/>
+&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">form_scope</span>.<br/>
+
+<br/>
+<span class="id" title="keyword">Notation</span> <a name="0fd935b7b481d69899ecb2c342d04bc9"><span class="id" title="notation">&quot;</span></a>[ 'new' 'Type' 'for' v ]" := (<a class="idref" href="mathcomp.ssreflect.eqtype.html#NewType"><span class="id" title="definition">NewType</span></a> <span class="id" title="var">v</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#vrefl_rect"><span class="id" title="definition">vrefl_rect</span></a>)<br/>
+&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "[ 'new' 'Type'  'for'  v ]") : <span class="id" title="var">form_scope</span>.<br/>
+
+<br/>
+<span class="id" title="keyword">Notation</span> <a name="bc8a10fee9a569270034af41e71a6ef6"><span class="id" title="notation">&quot;</span></a>[ 'newType' 'for' v 'by' rec ]" := (<a class="idref" href="mathcomp.ssreflect.eqtype.html#NewType"><span class="id" title="definition">NewType</span></a> <span class="id" title="var">v</span> <span class="id" title="var">_</span> <span class="id" title="keyword">rec</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#vrefl"><span class="id" title="lemma">vrefl</span></a>)<br/>
+&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "[ 'newType'  'for'  v  'by'  rec ]") : <span class="id" title="var">form_scope</span>.<br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="innew"><span class="id" title="definition">innew</span></a> <span class="id" title="var">T</span> <span class="id" title="var">nT</span> <span class="id" title="var">x</span> := @<a class="idref" href="mathcomp.ssreflect.eqtype.html#Sub"><span class="id" title="projection">Sub</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#T"><span class="id" title="variable">T</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#predT"><span class="id" title="definition">predT</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#nT"><span class="id" title="variable">nT</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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.ssrfun.html#erefl"><span class="id" title="abbreviation">erefl</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/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="innew_val"><span class="id" title="lemma">innew_val</span></a> <span class="id" title="var">T</span> <span class="id" title="var">nT</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#cancel"><span class="id" title="definition">cancel</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> (@<a class="idref" href="mathcomp.ssreflect.eqtype.html#innew"><span class="id" title="definition">innew</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#T"><span class="id" title="variable">T</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#nT"><span class="id" title="variable">nT</span></a>).<br/>
+ 
+<br/>
+</div>
+
+<div class="doc">
+ Prenex Implicits and renaming.  
+</div>
+<div class="code">
+<span class="id" title="keyword">Notation</span> <a name="sval"><span class="id" title="abbreviation">sval</span></a> := (@<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#proj1_sig"><span class="id" title="definition">proj1_sig</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span>).<br/>
+<span class="id" title="keyword">Notation</span> <a name="d31b79d69771a17d323737857541bcbd"><span class="id" title="notation">&quot;</span></a>@ 'sval'" := (@<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#proj1_sig"><span class="id" title="definition">proj1_sig</span></a>) (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 10, <span class="id" title="var">format</span> "@ 'sval'").<br/>
+
+<br/>
+<span class="id" title="keyword">Section</span> <a name="SigProj"><span class="id" title="section">SigProj</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Variables</span> (<a name="SigProj.T"><span class="id" title="variable">T</span></a> : <span class="id" title="keyword">Type</span>) (<a name="SigProj.P"><span class="id" title="variable">P</span></a> <a name="SigProj.Q"><span class="id" title="variable">Q</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#T"><span class="id" title="variable">T</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> <span class="id" title="keyword">Prop</span>).<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="svalP"><span class="id" title="lemma">svalP</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">u</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#sig"><span class="id" title="inductive">sig</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#SigProj.P"><span class="id" title="variable">P</span></a>, <a class="idref" href="mathcomp.ssreflect.eqtype.html#SigProj.P"><span class="id" title="variable">P</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#sval"><span class="id" title="abbreviation">sval</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#u"><span class="id" title="variable">u</span></a>).  <br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="s2val"><span class="id" title="definition">s2val</span></a> (<span class="id" title="var">u</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#sig2"><span class="id" title="inductive">sig2</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#SigProj.P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#SigProj.Q"><span class="id" title="variable">Q</span></a>) := <span class="id" title="keyword">let</span>: <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#exist2"><span class="id" title="constructor">exist2</span></a> <span class="id" title="var">x</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> := <a class="idref" href="mathcomp.ssreflect.eqtype.html#u"><span class="id" title="variable">u</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">x</span>.<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="s2valP"><span class="id" title="lemma">s2valP</span></a> <span class="id" title="var">u</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#SigProj.P"><span class="id" title="variable">P</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#s2val"><span class="id" title="definition">s2val</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#u"><span class="id" title="variable">u</span></a>).  <br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="s2valP'"><span class="id" title="lemma">s2valP'</span></a> <span class="id" title="var">u</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#SigProj.Q"><span class="id" title="variable">Q</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#s2val"><span class="id" title="definition">s2val</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#u"><span class="id" title="variable">u</span></a>).  <br/>
+
+<br/>
+<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#SigProj"><span class="id" title="section">SigProj</span></a>.<br/>
+
+<br/>
+
+<br/>
+<span class="id" title="keyword">Canonical</span> <span class="id" title="var">sig_subType</span> <span class="id" title="var">T</span> (<span class="id" title="var">P</span> : <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.ssreflect.eqtype.html#T"><span class="id" title="variable">T</span></a>) : <a class="idref" href="mathcomp.ssreflect.eqtype.html#subType"><span class="id" title="record">subType</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3f6d75f5a9cb81b61e8423a7aac22056"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3f6d75f5a9cb81b61e8423a7aac22056"><span class="id" title="notation">eta</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#P"><span class="id" title="variable">P</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3f6d75f5a9cb81b61e8423a7aac22056"><span class="id" title="notation">]</span></a> :=<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#341c160c3e7b20d967b85d1852a7f89f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#341c160c3e7b20d967b85d1852a7f89f"><span class="id" title="notation">subType</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#341c160c3e7b20d967b85d1852a7f89f"><span class="id" title="notation">for</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#d31b79d69771a17d323737857541bcbd"><span class="id" title="notation">@</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#d31b79d69771a17d323737857541bcbd"><span class="id" title="notation">sval</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#d31b79d69771a17d323737857541bcbd"><span class="id" title="notation">T</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#d31b79d69771a17d323737857541bcbd"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#d31b79d69771a17d323737857541bcbd"><span class="id" title="notation">eta</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#d31b79d69771a17d323737857541bcbd"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#d31b79d69771a17d323737857541bcbd"><span class="id" title="notation">eta</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#d31b79d69771a17d323737857541bcbd"><span class="id" title="notation">P</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#d31b79d69771a17d323737857541bcbd"><span class="id" title="notation">]]</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#341c160c3e7b20d967b85d1852a7f89f"><span class="id" title="notation">]</span></a>.<br/>
+
+<br/>
+</div>
+
+<div class="doc">
+ Shorthand for sigma types over collective predicates.  
+</div>
+<div class="code">
+<span class="id" title="keyword">Notation</span> <a name="1a455bcaee5ea445f350e97edcdae0a7"><span class="id" title="notation">&quot;</span></a>{ x 'in' A }" := <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#5b63cb9ed0fed82566685c66e56592e4"><span class="id" title="notation">{</span></a><span class="id" title="var">x</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#5b63cb9ed0fed82566685c66e56592e4"><span class="id" title="notation">|</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#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> <span class="id" title="var">A</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#5b63cb9ed0fed82566685c66e56592e4"><span class="id" title="notation">}</span></a><br/>
+&nbsp;&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">x</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">format</span>  "{ x  'in'  A }") : <span class="id" title="var">type_scope</span>.<br/>
+<span class="id" title="keyword">Notation</span> <a name="90ff5fc7f9623a792138a168eb90e748"><span class="id" title="notation">&quot;</span></a>{ x 'in' A | P }" := <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#5b63cb9ed0fed82566685c66e56592e4"><span class="id" title="notation">{</span></a><span class="id" title="var">x</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#5b63cb9ed0fed82566685c66e56592e4"><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><span class="id" title="var">x</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> <span class="id" title="var">A</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> <span class="id" title="var">P</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#5b63cb9ed0fed82566685c66e56592e4"><span class="id" title="notation">}</span></a><br/>
+&nbsp;&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">x</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">format</span>  "{ x  'in'  A  |  P }") : <span class="id" title="var">type_scope</span>.<br/>
+
+<br/>
+</div>
+
+<div class="doc">
+ Shorthand for the return type of insub.  
+</div>
+<div class="code">
+<span class="id" title="keyword">Notation</span> <a name="e96270cc06a082f346fc67858ed5d7e8"><span class="id" title="notation">&quot;</span></a>{ ? x : T | P }" := (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#option"><span class="id" title="inductive">option</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#72ca3fac4636a1b19c963b12162882cf"><span class="id" title="notation">{</span></a><span class="id" title="var">x</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#72ca3fac4636a1b19c963b12162882cf"><span class="id" title="notation">:</span></a> <span class="id" title="var">T</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#72ca3fac4636a1b19c963b12162882cf"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#is_true"><span class="id" title="definition">is_true</span></a> <span class="id" title="var">P</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#72ca3fac4636a1b19c963b12162882cf"><span class="id" title="notation">}</span></a>)<br/>
+&nbsp;&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">x</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">type_scope</span>.<br/>
+<span class="id" title="keyword">Notation</span> <a name="addfbab002f749a52fe38aa5d236c15e"><span class="id" title="notation">&quot;</span></a>{ ? x | P }" := <a class="idref" href="mathcomp.ssreflect.eqtype.html#e96270cc06a082f346fc67858ed5d7e8"><span class="id" title="notation">{?</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#e96270cc06a082f346fc67858ed5d7e8"><span class="id" title="notation">:</span></a> <span class="id" title="var">_</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#e96270cc06a082f346fc67858ed5d7e8"><span class="id" title="notation">|</span></a> <span class="id" title="var">P</span><a class="idref" href="mathcomp.ssreflect.eqtype.html#e96270cc06a082f346fc67858ed5d7e8"><span class="id" title="notation">}</span></a><br/>
+&nbsp;&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">x</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">format</span>  "{ ?  x  |  P }") : <span class="id" title="var">type_scope</span>.<br/>
+<span class="id" title="keyword">Notation</span> <a name="46be042940e532a3ee150602e617da0f"><span class="id" title="notation">&quot;</span></a>{ ? x 'in' A }" := <a class="idref" href="mathcomp.ssreflect.eqtype.html#addfbab002f749a52fe38aa5d236c15e"><span class="id" title="notation">{?</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#addfbab002f749a52fe38aa5d236c15e"><span class="id" title="notation">|</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#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> <span class="id" title="var">A</span><a class="idref" href="mathcomp.ssreflect.eqtype.html#addfbab002f749a52fe38aa5d236c15e"><span class="id" title="notation">}</span></a><br/>
+&nbsp;&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">x</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">format</span>  "{ ?  x  'in'  A }") : <span class="id" title="var">type_scope</span>.<br/>
+<span class="id" title="keyword">Notation</span> <a name="0c327e4c7a0e26b1f0e239d4b8334a50"><span class="id" title="notation">&quot;</span></a>{ ? x 'in' A | P }" := <a class="idref" href="mathcomp.ssreflect.eqtype.html#addfbab002f749a52fe38aa5d236c15e"><span class="id" title="notation">{?</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#addfbab002f749a52fe38aa5d236c15e"><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><span class="id" title="var">x</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> <span class="id" title="var">A</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> <span class="id" title="var">P</span><a class="idref" href="mathcomp.ssreflect.eqtype.html#addfbab002f749a52fe38aa5d236c15e"><span class="id" title="notation">}</span></a><br/>
+&nbsp;&nbsp;(<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">x</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">format</span>  "{ ?  x  'in'  A  |  P }") : <span class="id" title="var">type_scope</span>.<br/>
+
+<br/>
+</div>
+
+<div class="doc">
+ A variant of injection with default that infers a collective predicate 
+ from the membership proof for the default value.                        
+</div>
+<div class="code">
+<span class="id" title="keyword">Definition</span> <a name="insigd"><span class="id" title="definition">insigd</span></a> <span class="id" title="var">T</span> (<span class="id" title="var">A</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#mem_pred"><span class="id" title="inductive">mem_pred</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#T"><span class="id" title="variable">T</span></a>) <span class="id" title="var">x</span> (<span class="id" title="var">Ax</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#in_mem"><span class="id" title="definition">in_mem</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#A"><span class="id" title="variable">A</span></a>) :=<br/>
+&nbsp;&nbsp;<a class="idref" href="mathcomp.ssreflect.eqtype.html#insubd"><span class="id" title="definition">insubd</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#exist"><span class="id" title="constructor">exist</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3f6d75f5a9cb81b61e8423a7aac22056"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3f6d75f5a9cb81b61e8423a7aac22056"><span class="id" title="notation">eta</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3f6d75f5a9cb81b61e8423a7aac22056"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#Ax"><span class="id" title="variable">Ax</span></a>).<br/>
+
+<br/>
+</div>
+
+<div class="doc">
+ There should be a rel definition for the subType equality op, but this 
+ seems to cause the simpl tactic to diverge on expressions involving == 
+ on 4+ nested subTypes in a "strict" position (e.g., after ~~).         
+ Definition feq f := [rel x y | f x == f y].                             
+</div>
+<div class="code">
+
+<br/>
+<span class="id" title="keyword">Section</span> <a name="TransferEqType"><span class="id" title="section">TransferEqType</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Variables</span> (<a name="TransferEqType.T"><span class="id" title="variable">T</span></a> : <span class="id" title="keyword">Type</span>) (<a name="TransferEqType.eT"><span class="id" title="variable">eT</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#eqType"><span class="id" title="abbreviation">eqType</span></a>) (<a name="TransferEqType.f"><span class="id" title="variable">f</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#T"><span class="id" title="variable">T</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.ssreflect.eqtype.html#eT"><span class="id" title="variable">eT</span></a>).<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="inj_eqAxiom"><span class="id" title="lemma">inj_eqAxiom</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#TransferEqType.f"><span class="id" title="variable">f</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.ssreflect.eqtype.html#axiom"><span class="id" title="definition">Equality.axiom</span></a> (<span class="id" title="keyword">fun</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> ⇒ <a class="idref" href="mathcomp.ssreflect.eqtype.html#TransferEqType.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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.ssreflect.eqtype.html#TransferEqType.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#y"><span class="id" title="variable">y</span></a>).<br/>
+ 
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="InjEqMixin"><span class="id" title="definition">InjEqMixin</span></a> <span class="id" title="var">f_inj</span> := <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqMixin"><span class="id" title="abbreviation">EqMixin</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#inj_eqAxiom"><span class="id" title="lemma">inj_eqAxiom</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#f_inj"><span class="id" title="variable">f_inj</span></a>).<br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="PcanEqMixin"><span class="id" title="definition">PcanEqMixin</span></a> <span class="id" title="var">g</span> (<span class="id" title="var">fK</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#pcancel"><span class="id" title="definition">pcancel</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#TransferEqType.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#g"><span class="id" title="variable">g</span></a>) := <a class="idref" href="mathcomp.ssreflect.eqtype.html#InjEqMixin"><span class="id" title="definition">InjEqMixin</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#pcan_inj"><span class="id" title="lemma">pcan_inj</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#fK"><span class="id" title="variable">fK</span></a>).<br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="CanEqMixin"><span class="id" title="definition">CanEqMixin</span></a> <span class="id" title="var">g</span> (<span class="id" title="var">fK</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#cancel"><span class="id" title="definition">cancel</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#TransferEqType.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#g"><span class="id" title="variable">g</span></a>) := <a class="idref" href="mathcomp.ssreflect.eqtype.html#InjEqMixin"><span class="id" title="definition">InjEqMixin</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#can_inj"><span class="id" title="lemma">can_inj</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#fK"><span class="id" title="variable">fK</span></a>).<br/>
+
+<br/>
+<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#TransferEqType"><span class="id" title="section">TransferEqType</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Section</span> <a name="SubEqType"><span class="id" title="section">SubEqType</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Variables</span> (<a name="SubEqType.T"><span class="id" title="variable">T</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#eqType"><span class="id" title="abbreviation">eqType</span></a>) (<a name="SubEqType.P"><span class="id" title="variable">P</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.ssreflect.eqtype.html#T"><span class="id" title="variable">T</span></a>) (<a name="SubEqType.sT"><span class="id" title="variable">sT</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#subType"><span class="id" title="record">subType</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#P"><span class="id" title="variable">P</span></a>).<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="val_eqP"><span class="id" title="lemma">val_eqP</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#ev_ax"><span class="id" title="abbreviation">ev_ax</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#SubEqType.sT"><span class="id" title="variable">sT</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a>.  <br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="sub_eqMixin"><span class="id" title="definition">sub_eqMixin</span></a> := <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqMixin"><span class="id" title="abbreviation">EqMixin</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#val_eqP"><span class="id" title="lemma">val_eqP</span></a>.<br/>
+<span class="id" title="keyword">Canonical</span> <span class="id" title="var">sub_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#EqType"><span class="id" title="abbreviation">EqType</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#SubEqType.sT"><span class="id" title="variable">sT</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#sub_eqMixin"><span class="id" title="definition">sub_eqMixin</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="SubEqMixin"><span class="id" title="definition">SubEqMixin</span></a> :=<br/>
+&nbsp;&nbsp;(<span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.ssreflect.eqtype.html#SubType"><span class="id" title="constructor">SubType</span></a> <span class="id" title="var">_</span> <span class="id" title="var">v</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="keyword">as</span> <span class="id" title="var">sT'</span> := <a class="idref" href="mathcomp.ssreflect.eqtype.html#SubEqType.sT"><span class="id" title="variable">sT</span></a><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="id" title="keyword">return</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#ev_ax"><span class="id" title="abbreviation">ev_ax</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#sT'"><span class="id" title="variable">sT'</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</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.ssreflect.eqtype.html#class_of"><span class="id" title="abbreviation">Equality.class_of</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#sT'"><span class="id" title="variable">sT'</span></a> <span class="id" title="tactic">in</span><br/>
+&nbsp;&nbsp;&nbsp;<span class="id" title="keyword">fun</span> <span class="id" title="var">vP</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#ev_ax"><span class="id" title="abbreviation">ev_ax</span></a> <span class="id" title="var">_</span> <span class="id" title="var">v</span> ⇒ <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqMixin"><span class="id" title="abbreviation">EqMixin</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#vP"><span class="id" title="variable">vP</span></a><br/>
+&nbsp;&nbsp;&nbsp;) <a class="idref" href="mathcomp.ssreflect.eqtype.html#val_eqP"><span class="id" title="lemma">val_eqP</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="val_eqE"><span class="id" title="lemma">val_eqE</span></a> (<span class="id" title="var">u</span> <span class="id" title="var">v</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#SubEqType.sT"><span class="id" title="variable">sT</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.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#val"><span class="id" title="projection">val</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#v"><span class="id" title="variable">v</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.ssreflect.eqtype.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#v"><span class="id" title="variable">v</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">End</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#SubEqType"><span class="id" title="section">SubEqType</span></a>.<br/>
+
+<br/>
+
+<br/>
+<span class="id" title="keyword">Notation</span> <a name="4bc2d2dce12edef0fb9c71d4a902ae5d"><span class="id" title="notation">&quot;</span></a>[ 'eqMixin' 'of' T 'by' &lt;: ]" := (<a class="idref" href="mathcomp.ssreflect.eqtype.html#SubEqMixin"><span class="id" title="definition">SubEqMixin</span></a> <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssreflect.html#4509b22bf26e3d6d771897e22bd8bc8f"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#class_of"><span class="id" title="abbreviation">Equality.class_of</span></a> <span class="id" title="var">T</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> "[ 'eqMixin'  'of'  T  'by'  &lt;: ]") : <span class="id" title="var">form_scope</span>.<br/>
+
+<br/>
+<span class="id" title="keyword">Section</span> <a name="SigEqType"><span class="id" title="section">SigEqType</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Variables</span> (<a name="SigEqType.T"><span class="id" title="variable">T</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#eqType"><span class="id" title="abbreviation">eqType</span></a>) (<a name="SigEqType.P"><span class="id" title="variable">P</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.ssreflect.eqtype.html#T"><span class="id" title="variable">T</span></a>).<br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="sig_eqMixin"><span class="id" title="definition">sig_eqMixin</span></a> := <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#4bc2d2dce12edef0fb9c71d4a902ae5d"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#4bc2d2dce12edef0fb9c71d4a902ae5d"><span class="id" title="notation">eqMixin</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#4bc2d2dce12edef0fb9c71d4a902ae5d"><span class="id" title="notation">of</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#5b63cb9ed0fed82566685c66e56592e4"><span class="id" title="notation">{</span></a><span class="id" title="var">x</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#5b63cb9ed0fed82566685c66e56592e4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#SigEqType.P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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.Specif.html#5b63cb9ed0fed82566685c66e56592e4"><span class="id" title="notation">}</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#4bc2d2dce12edef0fb9c71d4a902ae5d"><span class="id" title="notation">by</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#4bc2d2dce12edef0fb9c71d4a902ae5d"><span class="id" title="notation">&lt;:]</span></a>.<br/>
+<span class="id" title="keyword">Canonical</span> <span class="id" title="var">sig_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#EqType"><span class="id" title="abbreviation">EqType</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#5b63cb9ed0fed82566685c66e56592e4"><span class="id" title="notation">{</span></a><span class="id" title="var">x</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#5b63cb9ed0fed82566685c66e56592e4"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#SigEqType.P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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.Specif.html#5b63cb9ed0fed82566685c66e56592e4"><span class="id" title="notation">}</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#sig_eqMixin"><span class="id" title="definition">sig_eqMixin</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#SigEqType"><span class="id" title="section">SigEqType</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Section</span> <a name="ProdEqType"><span class="id" title="section">ProdEqType</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Variable</span> <a name="ProdEqType.T1"><span class="id" title="variable">T1</span></a> <a name="ProdEqType.T2"><span class="id" title="variable">T2</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#eqType"><span class="id" title="abbreviation">eqType</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="pair_eq"><span class="id" title="definition">pair_eq</span></a> := <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#a3fa885266d530b93c1b9f67891df8e8"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#a3fa885266d530b93c1b9f67891df8e8"><span class="id" title="notation">rel</span></a> <span class="id" title="var">u</span> <span class="id" title="var">v</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#a3fa885266d530b93c1b9f67891df8e8"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#ProdEqType.T1"><span class="id" title="variable">T1</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.ssreflect.eqtype.html#ProdEqType.T2"><span class="id" title="variable">T2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#a3fa885266d530b93c1b9f67891df8e8"><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.ssreflect.eqtype.html#u"><span class="id" title="variable">u</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#c4877bbfe60d8f22b47ac99ace86216a"><span class="id" title="notation">.1</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#v"><span class="id" title="variable">v</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#c4877bbfe60d8f22b47ac99ace86216a"><span class="id" title="notation">.1</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.ssreflect.eqtype.html#u"><span class="id" title="variable">u</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#f4827404159513e7fd691b60b7877737"><span class="id" title="notation">.2</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#v"><span class="id" title="variable">v</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#f4827404159513e7fd691b60b7877737"><span class="id" title="notation">.2</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.ssr.ssrbool.html#a3fa885266d530b93c1b9f67891df8e8"><span class="id" title="notation">]</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="pair_eqP"><span class="id" title="lemma">pair_eqP</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#axiom"><span class="id" title="definition">Equality.axiom</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#pair_eq"><span class="id" title="definition">pair_eq</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="prod_eqMixin"><span class="id" title="definition">prod_eqMixin</span></a> := <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqMixin"><span class="id" title="abbreviation">EqMixin</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#pair_eqP"><span class="id" title="lemma">pair_eqP</span></a>.<br/>
+<span class="id" title="keyword">Canonical</span> <span class="id" title="var">prod_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#EqType"><span class="id" title="abbreviation">EqType</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#ProdEqType.T1"><span class="id" title="variable">T1</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.ssreflect.eqtype.html#ProdEqType.T2"><span class="id" title="variable">T2</span></a>) <a class="idref" href="mathcomp.ssreflect.eqtype.html#prod_eqMixin"><span class="id" title="definition">prod_eqMixin</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="pair_eqE"><span class="id" title="lemma">pair_eqE</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#pair_eq"><span class="id" title="definition">pair_eq</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#8f9364556521ebb498093f28eea2240f"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#eq_op"><span class="id" title="definition">eq_op</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#8f9364556521ebb498093f28eea2240f"><span class="id" title="notation">:&gt;</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#rel"><span class="id" title="definition">rel</span></a> <span class="id" title="var">_</span>.  <br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="xpair_eqE"><span class="id" title="lemma">xpair_eqE</span></a> (<span class="id" title="var">x1</span> <span class="id" title="var">y1</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#ProdEqType.T1"><span class="id" title="variable">T1</span></a>) (<span class="id" title="var">x2</span> <span class="id" title="var">y2</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#ProdEqType.T2"><span class="id" title="variable">T2</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="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.ssreflect.eqtype.html#x1"><span class="id" title="variable">x1</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.ssreflect.eqtype.html#x2"><span class="id" title="variable">x2</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.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</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.ssreflect.eqtype.html#y1"><span class="id" title="variable">y1</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.ssreflect.eqtype.html#y2"><span class="id" title="variable">y2</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="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="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.ssreflect.eqtype.html#x1"><span class="id" title="variable">x1</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#y1"><span class="id" title="variable">y1</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.ssreflect.eqtype.html#x2"><span class="id" title="variable">x2</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#y2"><span class="id" title="variable">y2</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.Logic.html#1c39bf18749e5cc609e83c0a0ba5a372"><span class="id" title="notation">)</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="pair_eq1"><span class="id" title="lemma">pair_eq1</span></a> (<span class="id" title="var">u</span> <span class="id" title="var">v</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#ProdEqType.T1"><span class="id" title="variable">T1</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.ssreflect.eqtype.html#ProdEqType.T2"><span class="id" title="variable">T2</span></a>) : <a class="idref" href="mathcomp.ssreflect.eqtype.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#v"><span class="id" title="variable">v</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.ssreflect.eqtype.html#u"><span class="id" title="variable">u</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#c4877bbfe60d8f22b47ac99ace86216a"><span class="id" title="notation">.1</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#v"><span class="id" title="variable">v</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#c4877bbfe60d8f22b47ac99ace86216a"><span class="id" title="notation">.1</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="pair_eq2"><span class="id" title="lemma">pair_eq2</span></a> (<span class="id" title="var">u</span> <span class="id" title="var">v</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#ProdEqType.T1"><span class="id" title="variable">T1</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.ssreflect.eqtype.html#ProdEqType.T2"><span class="id" title="variable">T2</span></a>) : <a class="idref" href="mathcomp.ssreflect.eqtype.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#v"><span class="id" title="variable">v</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.ssreflect.eqtype.html#u"><span class="id" title="variable">u</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#f4827404159513e7fd691b60b7877737"><span class="id" title="notation">.2</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#v"><span class="id" title="variable">v</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#f4827404159513e7fd691b60b7877737"><span class="id" title="notation">.2</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#ProdEqType"><span class="id" title="section">ProdEqType</span></a>.<br/>
+
+<br/>
+
+<br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="predX"><span class="id" title="definition">predX</span></a> <span class="id" title="var">T1</span> <span class="id" title="var">T2</span> (<span class="id" title="var">p1</span> : <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.ssreflect.eqtype.html#T1"><span class="id" title="variable">T1</span></a>) (<span class="id" title="var">p2</span> : <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.ssreflect.eqtype.html#T2"><span class="id" title="variable">T2</span></a>) :=<br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#b8288f36a4177926116f8c7429ee1d26"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#b8288f36a4177926116f8c7429ee1d26"><span class="id" title="notation">pred</span></a> <span class="id" title="var">z</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#b8288f36a4177926116f8c7429ee1d26"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#p1"><span class="id" title="variable">p1</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#z"><span class="id" title="variable">z</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#c4877bbfe60d8f22b47ac99ace86216a"><span class="id" title="notation">.1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#b8288f36a4177926116f8c7429ee1d26"><span class="id" title="notation">&amp;</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#p2"><span class="id" title="variable">p2</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#z"><span class="id" title="variable">z</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#f4827404159513e7fd691b60b7877737"><span class="id" title="notation">.2</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#b8288f36a4177926116f8c7429ee1d26"><span class="id" title="notation">]</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Notation</span> <a name="a4c99a0dbc2a758b24afbd951fc3a580"><span class="id" title="notation">&quot;</span></a>[ 'predX' A1 &amp; A2 ]" := (<a class="idref" href="mathcomp.ssreflect.eqtype.html#predX"><span class="id" title="definition">predX</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#913cf87021a195b218018885aad8c94f"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#913cf87021a195b218018885aad8c94f"><span class="id" title="notation">mem</span></a> <span class="id" title="var">A1</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#913cf87021a195b218018885aad8c94f"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#913cf87021a195b218018885aad8c94f"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#913cf87021a195b218018885aad8c94f"><span class="id" title="notation">mem</span></a> <span class="id" title="var">A2</span><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrbool.html#913cf87021a195b218018885aad8c94f"><span class="id" title="notation">]</span></a>)<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> "[ 'predX'  A1  &amp;  A2 ]") : <span class="id" title="var">fun_scope</span>.<br/>
+
+<br/>
+<span class="id" title="keyword">Section</span> <a name="OptionEqType"><span class="id" title="section">OptionEqType</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Variable</span> <a name="OptionEqType.T"><span class="id" title="variable">T</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#eqType"><span class="id" title="abbreviation">eqType</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="opt_eq"><span class="id" title="definition">opt_eq</span></a> (<span class="id" title="var">u</span> <span class="id" title="var">v</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#option"><span class="id" title="inductive">option</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#OptionEqType.T"><span class="id" title="variable">T</span></a>) : <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> :=<br/>
+&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#oapp"><span class="id" title="abbreviation">oapp</span></a> (<span class="id" title="keyword">fun</span> <span class="id" title="var">x</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#oapp"><span class="id" title="abbreviation">oapp</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#eq_op"><span class="id" title="definition">eq_op</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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#false"><span class="id" title="constructor">false</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#v"><span class="id" title="variable">v</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.ssreflect.eqtype.html#v"><span class="id" title="variable">v</span></a>) <a class="idref" href="mathcomp.ssreflect.eqtype.html#u"><span class="id" title="variable">u</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="opt_eqP"><span class="id" title="lemma">opt_eqP</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#axiom"><span class="id" title="definition">Equality.axiom</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#opt_eq"><span class="id" title="definition">opt_eq</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Canonical</span> <span class="id" title="var">option_eqMixin</span> := <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqMixin"><span class="id" title="abbreviation">EqMixin</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#opt_eqP"><span class="id" title="lemma">opt_eqP</span></a>.<br/>
+<span class="id" title="keyword">Canonical</span> <span class="id" title="var">option_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#EqType"><span class="id" title="abbreviation">EqType</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#option"><span class="id" title="inductive">option</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#OptionEqType.T"><span class="id" title="variable">T</span></a>) <a class="idref" href="mathcomp.ssreflect.eqtype.html#option_eqMixin"><span class="id" title="definition">option_eqMixin</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#OptionEqType"><span class="id" title="section">OptionEqType</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="tag"><span class="id" title="definition">tag</span></a> := <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#projS1"><span class="id" title="abbreviation">projS1</span></a>.<br/>
+<span class="id" title="keyword">Definition</span> <a name="tagged"><span class="id" title="definition">tagged</span></a> <span class="id" title="var">I</span> <span class="id" title="var">T_</span> :  <span class="id" title="keyword">∀</span> <span class="id" title="var">u</span>, <a class="idref" href="mathcomp.ssreflect.eqtype.html#T_"><span class="id" title="variable">T_</span></a>(<a class="idref" href="mathcomp.ssreflect.eqtype.html#tag"><span class="id" title="definition">tag</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#u"><span class="id" title="variable">u</span></a>) := @<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#projS2"><span class="id" title="abbreviation">projS2</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#I"><span class="id" title="variable">I</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3f6d75f5a9cb81b61e8423a7aac22056"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3f6d75f5a9cb81b61e8423a7aac22056"><span class="id" title="notation">eta</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#T_"><span class="id" title="variable">T_</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3f6d75f5a9cb81b61e8423a7aac22056"><span class="id" title="notation">]</span></a>.<br/>
+<span class="id" title="keyword">Definition</span> <a name="Tagged"><span class="id" title="definition">Tagged</span></a> <span class="id" title="var">I</span> <span class="id" title="var">i</span> <span class="id" title="var">T_</span> <span class="id" title="var">x</span> := @<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#existS"><span class="id" title="abbreviation">existS</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#I"><span class="id" title="variable">I</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3f6d75f5a9cb81b61e8423a7aac22056"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3f6d75f5a9cb81b61e8423a7aac22056"><span class="id" title="notation">eta</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#T_"><span class="id" title="variable">T_</span></a><a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.ssr.ssrfun.html#3f6d75f5a9cb81b61e8423a7aac22056"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Section</span> <a name="TaggedAs"><span class="id" title="section">TaggedAs</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Variables</span> (<a name="TaggedAs.I"><span class="id" title="variable">I</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#eqType"><span class="id" title="abbreviation">eqType</span></a>) (<a name="TaggedAs.T_"><span class="id" title="variable">T_</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.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> <span class="id" title="keyword">Type</span>).<br/>
+<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> <span class="id" title="var">u</span> <span class="id" title="var">v</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#50b5d8dd6be4fba768e35617e518ad76"><span class="id" title="notation">{</span></a><span class="id" title="var">i</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#50b5d8dd6be4fba768e35617e518ad76"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#TaggedAs.I"><span class="id" title="variable">I</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#50b5d8dd6be4fba768e35617e518ad76"><span class="id" title="notation">&amp;</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#TaggedAs.T_"><span class="id" title="variable">T_</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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.Specif.html#50b5d8dd6be4fba768e35617e518ad76"><span class="id" title="notation">}</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="tagged_as"><span class="id" title="definition">tagged_as</span></a> <span class="id" title="var">u</span> <span class="id" title="var">v</span> :=<br/>
+&nbsp;&nbsp;<span class="id" title="keyword">if</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#tag"><span class="id" title="definition">tag</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#ab7a7bc39754581ab8f205db64711d57"><span class="id" title="notation">=</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#ab7a7bc39754581ab8f205db64711d57"><span class="id" title="notation">P</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#tag"><span class="id" title="definition">tag</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#v"><span class="id" title="variable">v</span></a> <span class="id" title="keyword">is</span> <span class="id" title="var">ReflectT</span> <span class="id" title="var">eq_uv</span> <span class="id" title="keyword">then</span><br/>
+&nbsp;&nbsp;&nbsp;&nbsp;<a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Logic.html#eq_rect_r"><span class="id" title="definition">eq_rect_r</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#TaggedAs.T_"><span class="id" title="variable">T_</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#tagged"><span class="id" title="definition">tagged</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#v"><span class="id" title="variable">v</span></a>) <span class="id" title="var">eq_uv</span><br/>
+&nbsp;&nbsp;<span class="id" title="keyword">else</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#tagged"><span class="id" title="definition">tagged</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#u"><span class="id" title="variable">u</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="tagged_asE"><span class="id" title="lemma">tagged_asE</span></a> <span class="id" title="var">u</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#tagged_as"><span class="id" title="definition">tagged_as</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#u"><span class="id" title="variable">u</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#Tagged"><span class="id" title="definition">Tagged</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#TaggedAs.T_"><span class="id" title="variable">T_</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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="mathcomp.ssreflect.eqtype.html#x"><span class="id" title="variable">x</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#TaggedAs"><span class="id" title="section">TaggedAs</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Section</span> <a name="TagEqType"><span class="id" title="section">TagEqType</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Variables</span> (<a name="TagEqType.I"><span class="id" title="variable">I</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#eqType"><span class="id" title="abbreviation">eqType</span></a>) (<a name="TagEqType.T_"><span class="id" title="variable">T_</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.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="mathcomp.ssreflect.eqtype.html#eqType"><span class="id" title="abbreviation">eqType</span></a>).<br/>
+<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> <span class="id" title="var">u</span> <span class="id" title="var">v</span> : <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#50b5d8dd6be4fba768e35617e518ad76"><span class="id" title="notation">{</span></a><span class="id" title="var">i</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#50b5d8dd6be4fba768e35617e518ad76"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#TagEqType.I"><span class="id" title="variable">I</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#50b5d8dd6be4fba768e35617e518ad76"><span class="id" title="notation">&amp;</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#TagEqType.T_"><span class="id" title="variable">T_</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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.Specif.html#50b5d8dd6be4fba768e35617e518ad76"><span class="id" title="notation">}</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="tag_eq"><span class="id" title="definition">tag_eq</span></a> <span class="id" title="var">u</span> <span class="id" title="var">v</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="mathcomp.ssreflect.eqtype.html#tag"><span class="id" title="definition">tag</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#tag"><span class="id" title="definition">tag</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#v"><span class="id" title="variable">v</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.ssreflect.eqtype.html#tagged"><span class="id" title="definition">tagged</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#tagged_as"><span class="id" title="definition">tagged_as</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#v"><span class="id" title="variable">v</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/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="tag_eqP"><span class="id" title="lemma">tag_eqP</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#axiom"><span class="id" title="definition">Equality.axiom</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#tag_eq"><span class="id" title="definition">tag_eq</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Canonical</span> <span class="id" title="var">tag_eqMixin</span> := <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqMixin"><span class="id" title="abbreviation">EqMixin</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#tag_eqP"><span class="id" title="lemma">tag_eqP</span></a>.<br/>
+<span class="id" title="keyword">Canonical</span> <span class="id" title="var">tag_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#EqType"><span class="id" title="abbreviation">EqType</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#50b5d8dd6be4fba768e35617e518ad76"><span class="id" title="notation">{</span></a><span class="id" title="var">i</span> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#50b5d8dd6be4fba768e35617e518ad76"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#TagEqType.I"><span class="id" title="variable">I</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Specif.html#50b5d8dd6be4fba768e35617e518ad76"><span class="id" title="notation">&amp;</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#TagEqType.T_"><span class="id" title="variable">T_</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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.Specif.html#50b5d8dd6be4fba768e35617e518ad76"><span class="id" title="notation">}</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#tag_eqMixin"><span class="id" title="definition">tag_eqMixin</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="tag_eqE"><span class="id" title="lemma">tag_eqE</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#tag_eq"><span class="id" title="definition">tag_eq</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.ssreflect.eqtype.html#eq_op"><span class="id" title="definition">eq_op</span></a>.  <br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="eq_tag"><span class="id" title="lemma">eq_tag</span></a> <span class="id" title="var">u</span> <span class="id" title="var">v</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#v"><span class="id" title="variable">v</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.ssreflect.eqtype.html#tag"><span class="id" title="definition">tag</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#u"><span class="id" title="variable">u</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.ssreflect.eqtype.html#tag"><span class="id" title="definition">tag</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#v"><span class="id" title="variable">v</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="eq_Tagged"><span class="id" title="lemma">eq_Tagged</span></a> <span class="id" title="var">u</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><a class="idref" href="mathcomp.ssreflect.eqtype.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#Tagged"><span class="id" title="definition">Tagged</span></a> <span class="id" title="var">_</span> <a class="idref" href="mathcomp.ssreflect.eqtype.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="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.ssreflect.eqtype.html#tagged"><span class="id" title="definition">tagged</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#u"><span class="id" title="variable">u</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.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/>
+ 
+<br/>
+<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#TagEqType"><span class="id" title="section">TagEqType</span></a>.<br/>
+
+<br/>
+
+<br/>
+<span class="id" title="keyword">Section</span> <a name="SumEqType"><span class="id" title="section">SumEqType</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Variables</span> <a name="SumEqType.T1"><span class="id" title="variable">T1</span></a> <a name="SumEqType.T2"><span class="id" title="variable">T2</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#eqType"><span class="id" title="abbreviation">eqType</span></a>.<br/>
+<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> <span class="id" title="var">u</span> <span class="id" title="var">v</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#SumEqType.T1"><span class="id" title="variable">T1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#3dcaec3b772747610227247939f96b01"><span class="id" title="notation">+</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#SumEqType.T2"><span class="id" title="variable">T2</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Definition</span> <a name="sum_eq"><span class="id" title="definition">sum_eq</span></a> <span class="id" title="var">u</span> <span class="id" title="var">v</span> :=<br/>
+&nbsp;&nbsp;<span class="id" title="keyword">match</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#u"><span class="id" title="variable">u</span></a>, <a class="idref" href="mathcomp.ssreflect.eqtype.html#v"><span class="id" title="variable">v</span></a> <span class="id" title="keyword">with</span><br/>
+&nbsp;&nbsp;| <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#inl"><span class="id" title="constructor">inl</span></a> <span class="id" title="var">x</span>, <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#inl"><span class="id" title="constructor">inl</span></a> <span class="id" title="var">y</span> | <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#inr"><span class="id" title="constructor">inr</span></a> <span class="id" title="var">x</span>, <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#inr"><span class="id" title="constructor">inr</span></a> <span class="id" title="var">y</span> ⇒ <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#17d28d004d0863cb022d4ce832ddaaae"><span class="id" title="notation">==</span></a> <span class="id" title="var">y</span><br/>
+&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#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="sum_eqP"><span class="id" title="lemma">sum_eqP</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#axiom"><span class="id" title="definition">Equality.axiom</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#sum_eq"><span class="id" title="definition">sum_eq</span></a>.<br/>
+ 
+<br/>
+<span class="id" title="keyword">Canonical</span> <span class="id" title="var">sum_eqMixin</span> := <a class="idref" href="mathcomp.ssreflect.eqtype.html#EqMixin"><span class="id" title="abbreviation">EqMixin</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#sum_eqP"><span class="id" title="lemma">sum_eqP</span></a>.<br/>
+<span class="id" title="keyword">Canonical</span> <span class="id" title="var">sum_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#EqType"><span class="id" title="abbreviation">EqType</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#SumEqType.T1"><span class="id" title="variable">T1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/8.8.0/stdlib//Coq.Init.Datatypes.html#3dcaec3b772747610227247939f96b01"><span class="id" title="notation">+</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#SumEqType.T2"><span class="id" title="variable">T2</span></a>) <a class="idref" href="mathcomp.ssreflect.eqtype.html#sum_eqMixin"><span class="id" title="definition">sum_eqMixin</span></a>.<br/>
+
+<br/>
+<span class="id" title="keyword">Lemma</span> <a name="sum_eqE"><span class="id" title="lemma">sum_eqE</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#sum_eq"><span class="id" title="definition">sum_eq</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.ssreflect.eqtype.html#eq_op"><span class="id" title="definition">eq_op</span></a>.  <br/>
+
+<br/>
+<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#SumEqType"><span class="id" title="section">SumEqType</span></a>.<br/>
+
+<br/>
+</div>
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author	Enrico Tassi	2018-04-20 10:54:22 +0200
committer	Enrico Tassi	2018-04-20 10:54:22 +0200
commit	ed05182cece6bb3706e09b2ce14af4a41a2e8141 (patch)
tree	e850d7314b6372d0476cf2ffaf7d3830721db7b1 /docs/htmldoc/mathcomp.ssreflect.eqtype.html
parent	3d196f44681fb3b23ff8a79fbd44e12308680531 (diff)