Remplacement des fichiers .v ancienne syntaxe de theories, contrib et states par les fichiers nouvelle syntaxe

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@5027 85f007b7-540e-0410-9357-904b9bb8a0f7

1 files changed, 33 insertions, 33 deletions

diff --git a/theories/Wellfounded/Well_Ordering.v b/theories/Wellfounded/Well_Ordering.v
index 49595dd2b..c4c7daa98 100644
--- a/theories/Wellfounded/Well_Ordering.v
+++ b/theories/Wellfounded/Well_Ordering.v
@@ -12,36 +12,36 @@
     From: Constructing Recursion Operators in Type Theory
     L. Paulson  JSC (1986) 2, 325-355 *)
 
-Require Eqdep.
+Require Import Eqdep.
 
 Section WellOrdering.
-Variable A:Set.
-Variable B:A->Set. 
+Variable A : Set.
+Variable B : A -> Set. 
 
 Inductive WO : Set :=
-   sup : (a:A)(f:(B a)->WO)WO.
+    sup : forall (a:A) (f:B a -> WO), WO.
 
 
-Inductive le_WO  : WO->WO->Prop :=
-  le_sup : (a:A)(f:(B a)->WO)(v:(B a)) (le_WO  (f v) (sup a f)).
+Inductive le_WO : WO -> WO -> Prop :=
+    le_sup : forall (a:A) (f:B a -> WO) (v:B a), le_WO (f v) (sup a f).
  
 
-Theorem wf_WO : (well_founded WO le_WO ).
+Theorem wf_WO : well_founded le_WO.
 Proof.
- Unfold well_founded ;Intro.
- Apply Acc_intro.
- Elim a.
- Intros.
- Inversion H0.
- Apply Acc_intro.
- Generalize H4 ;Generalize H1 ;Generalize f0 ;Generalize v.
- Rewrite -> H3.
- Intros.
- Apply (H v0 y0).
- Cut (eq ? f f1).
- Intros E;Rewrite -> E;Auto.
- Symmetry.
- Apply (inj_pair2 A [a0:A](B a0)->WO a0 f1 f H5).
+ unfold well_founded in |- *; intro.
+ apply Acc_intro.
+ elim a.
+ intros.
+ inversion H0.
+ apply Acc_intro.
+ generalize H4; generalize H1; generalize f0; generalize v.
+ rewrite H3.
+ intros.
+ apply (H v0 y0).
+ cut (f = f1).
+ intros E; rewrite E; auto.
+ symmetry  in |- *.
+ apply (inj_pair2 A (fun a0:A => B a0 -> WO) a0 f1 f H5).
 Qed.
 
 End WellOrdering.
@@ -53,20 +53,20 @@ Section Characterisation_wf_relations.
 (*  in course of development                                          *)
 
 
-Variable A:Set.
-Variable leA:A->A->Prop.
+Variable A : Set.
+Variable leA : A -> A -> Prop.
 
-Definition B:= [a:A] {x:A | (leA x a)}.
+Definition B (a:A) := {x : A | leA x a}.
 
-Definition  wof: (well_founded A leA)-> A-> (WO A B).
+Definition wof : well_founded leA -> A -> WO A B.
 Proof.
- Intros.
- Apply (well_founded_induction A leA H [a:A](WO A B));Auto.
- Intros.
- Apply (sup A B x).
- Unfold 1 B .
- NewDestruct 1 as [x0].
- Apply (H1 x0);Auto.
+ intros.
+ apply (well_founded_induction H (fun a:A => WO A B)); auto.
+ intros.
+ apply (sup A B x).
+ unfold B at 1 in |- *.
+ destruct 1 as [x0].
+ apply (H1 x0); auto.
 Qed.
 
-End Characterisation_wf_relations.
+End Characterisation_wf_relations.
\ No newline at end of file