Merge PR #12288: Prove that classical reals implement constructive reals.

Reviewed-by: MSoegtropIMC
Reviewed-by: Zimmi48

1 files changed, 31 insertions, 10 deletions

diff --git a/doc/stdlib/index-list.html.template b/doc/stdlib/index-list.html.template
index 426f67eb53..1a02d6e65d 100644
--- a/doc/stdlib/index-list.html.template
+++ b/doc/stdlib/index-list.html.template
@@ -540,18 +540,15 @@ through the <tt>Require Import</tt> command.</p>
     Formalization of real numbers
   </dt>
   <dd>
+    <dl> 
+  <dt> <b>Classical Reals</b>:
+    Real numbers with excluded middle, total order and least upper bounds
+  </dt>
+  <dd>
     theories/Reals/Rdefinitions.v
-    theories/Reals/Cauchy/ConstructiveCauchyReals.v
-    theories/Reals/Cauchy/ConstructiveCauchyRealsMult.v
-    theories/Reals/Cauchy/ConstructiveCauchyAbs.v
     theories/Reals/ClassicalDedekindReals.v
+    theories/Reals/ClassicalConstructiveReals.v
     theories/Reals/Raxioms.v
-    theories/Reals/Abstract/ConstructiveReals.v
-    theories/Reals/Abstract/ConstructiveRealsMorphisms.v
-    theories/Reals/Abstract/ConstructiveLUB.v
-    theories/Reals/Abstract/ConstructiveAbs.v
-    theories/Reals/Abstract/ConstructiveLimits.v
-    theories/Reals/Abstract/ConstructiveSum.v
     theories/Reals/RIneq.v
     theories/Reals/DiscrR.v
     theories/Reals/ROrderedType.v
@@ -597,7 +594,6 @@ through the <tt>Require Import</tt> command.</p>
     theories/Reals/Ranalysis5.v
     theories/Reals/Ranalysis_reg.v
     theories/Reals/Rcomplete.v
-    theories/Reals/Cauchy/ConstructiveRcomplete.v
     theories/Reals/RiemannInt.v
     theories/Reals/RiemannInt_SF.v
     theories/Reals/Rpow_def.v
@@ -617,6 +613,31 @@ through the <tt>Require Import</tt> command.</p>
     (theories/Reals/Reals.v)
     theories/Reals/Runcountable.v
   </dd>
+  <dt> <b>Abstract Constructive Reals</b>:
+    Interface of constructive reals, proof of equivalence of all implementations. EXPERIMENTAL 
+  </dt>
+  <dd>
+    theories/Reals/Abstract/ConstructiveReals.v
+    theories/Reals/Abstract/ConstructiveRealsMorphisms.v
+    theories/Reals/Abstract/ConstructiveLUB.v
+    theories/Reals/Abstract/ConstructiveAbs.v
+    theories/Reals/Abstract/ConstructiveLimits.v
+    theories/Reals/Abstract/ConstructiveMinMax.v
+    theories/Reals/Abstract/ConstructivePower.v
+    theories/Reals/Abstract/ConstructiveSum.v 
+  </dd>
+  <dt> <b>Constructive Cauchy Reals</b>:
+    Cauchy sequences of rational numbers, implementation of the interface. EXPERIMENTAL
+  </dt>
+  <dd>
+    theories/Reals/Cauchy/ConstructiveRcomplete.v
+    theories/Reals/Cauchy/ConstructiveCauchyReals.v
+    theories/Reals/Cauchy/ConstructiveCauchyRealsMult.v
+    theories/Reals/Cauchy/ConstructiveCauchyAbs.v
+  </dd>
+
+  </dl>
+  </dd>
 
   <dt> <b>Program</b>:
     Support for dependently-typed programming