portage Refine

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@559 85f007b7-540e-0410-9357-904b9bb8a0f7

2 files changed, 16 insertions, 8 deletions

diff --git a/theories/Lists/ListSet.v b/theories/Lists/ListSet.v
index 6de241d184..a1c86e78f6 100644
--- a/theories/Lists/ListSet.v
+++ b/theories/Lists/ListSet.v
@@ -7,14 +7,14 @@
 
 (* PolyList is loaded, but not exported *)
 (* This allow to "hide" the definitions, functions and theorems of PolyList
- and to see only the ones of ListSet *)
+   and to see only the ones of ListSet *)
+
 Require PolyList.
 
 Implicit Arguments On.
 
 Section first_definitions.
 
-
   Variable A : Set.
   Hypothesis Aeq_dec : (x,y:A){x=y}+{~x=y}.
 
@@ -87,10 +87,14 @@ Section first_definitions.
 
   Proof.
     Unfold set_In.
-    Realizer set_mem.
-    Program_all.
-    Rewrite e; Simpl; Auto with datatypes.
-    Simpl; Unfold not; Intros [Hc1 | Hc2 ]; Auto with datatypes.
+    (*** Realizer set_mem. Program_all. ***)
+    Induction x.
+    Auto.
+    Intros a0 x0 Ha0. Case (Aeq_dec a a0); Intro eq.
+    Rewrite eq; Simpl; Auto with datatypes.
+    Elim Ha0.
+    Auto with datatypes.
+    Right; Simpl; Unfold not; Intros [Hc1 | Hc2 ]; Auto with datatypes.
   Save.
 
   Lemma set_mem_ind : 
diff --git a/theories/Lists/PolyList.v b/theories/Lists/PolyList.v
index 1129e9af02..9638d4a214 100644
--- a/theories/Lists/PolyList.v
+++ b/theories/Lists/PolyList.v
@@ -386,8 +386,12 @@ Fixpoint nth_ok [n:nat; l:list] : A->bool :=
 
 Lemma nth_in_or_default :
   (n:nat)(l:list)(d:A){(In (nth n l d) l)}+{(nth n l d)=d}.
-Realizer nth_ok.
-Program_all.
+(** Realizer nth_ok. Program_all. **)
+Intros n l d; Generalize n; Induction l; Intro n0.
+Right; Case n0; Trivial.
+Case n0; Simpl.
+Auto.
+Intro n1; Elim (Hrecl n1); Auto.     
 Save.
 
 Lemma nth_S_cons :