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, 35 insertions, 29 deletions

diff --git a/theories/Logic/Classical_Pred_Type.v b/theories/Logic/Classical_Pred_Type.v
index 6745d05fd..6bfd08e43 100755
--- a/theories/Logic/Classical_Pred_Type.v
+++ b/theories/Logic/Classical_Pred_Type.v
@@ -10,55 +10,61 @@
 
 (** Classical Predicate Logic on Type *)
 
-Require Classical_Prop.
+Require Import Classical_Prop.
 
 Section Generic.
-Variable U: Type.
+Variable U : Type.
 
 (** de Morgan laws for quantifiers *)
 
-Lemma not_all_ex_not : (P:U->Prop)(~(n:U)(P n)) -> (EXT n:U | ~(P n)).
+Lemma not_all_ex_not :
+ forall P:U -> Prop, ~ (forall n:U, P n) ->  exists n : U | ~ P n.
 Proof.
-Unfold not; Intros P notall.
-Apply NNPP; Unfold not.
-Intro abs.
-Cut ((n:U)(P n)); Auto.
-Intro n; Apply NNPP.
-Unfold not; Intros.
-Apply abs; Exists n; Trivial.
+unfold not in |- *; intros P notall.
+apply NNPP; unfold not in |- *.
+intro abs.
+cut (forall n:U, P n); auto.
+intro n; apply NNPP.
+unfold not in |- *; intros.
+apply abs; exists n; trivial.
 Qed.
 
-Lemma not_all_not_ex : (P:U->Prop)(~(n:U)~(P n)) -> (EXT n:U | (P n)).
+Lemma not_all_not_ex :
+ forall P:U -> Prop, ~ (forall n:U, ~ P n) ->  exists n : U | P n.
 Proof.
-Intros P H.
-Elim (not_all_ex_not [n:U]~(P n) H); Intros n Pn; Exists n.
-Apply NNPP; Trivial.
+intros P H.
+elim (not_all_ex_not (fun n:U => ~ P n) H); intros n Pn; exists n.
+apply NNPP; trivial.
 Qed.
 
-Lemma not_ex_all_not : (P:U->Prop)(~(EXT n:U | (P n))) -> (n:U)~(P n).
+Lemma not_ex_all_not :
+ forall P:U -> Prop, ~ ( exists n : U | P n) -> forall n:U, ~ P n.
 Proof.
-Unfold not; Intros P notex n abs.
-Apply notex.
-Exists n; Trivial.
+unfold not in |- *; intros P notex n abs.
+apply notex.
+exists n; trivial.
 Qed. 
 
-Lemma not_ex_not_all : (P:U->Prop)(~(EXT n:U | ~(P n))) -> (n:U)(P n).
+Lemma not_ex_not_all :
+ forall P:U -> Prop, ~ ( exists n : U | ~ P n) -> forall n:U, P n.
 Proof.
-Intros P H n.
-Apply NNPP.
-Red; Intro K; Apply H; Exists n; Trivial.
+intros P H n.
+apply NNPP.
+red in |- *; intro K; apply H; exists n; trivial.
 Qed.
 
-Lemma ex_not_not_all : (P:U->Prop) (EXT n:U | ~(P n)) -> ~(n:U)(P n).
+Lemma ex_not_not_all :
+ forall P:U -> Prop, ( exists n : U | ~ P n) -> ~ (forall n:U, P n).
 Proof.
-Unfold not; Intros P exnot allP.
-Elim exnot; Auto.
+unfold not in |- *; intros P exnot allP.
+elim exnot; auto.
 Qed.
 
-Lemma all_not_not_ex : (P:U->Prop) ((n:U)~(P n)) -> ~(EXT n:U | (P n)).
+Lemma all_not_not_ex :
+ forall P:U -> Prop, (forall n:U, ~ P n) -> ~ ( exists n : U | P n).
 Proof.
-Unfold not; Intros P allnot exP; Elim exP; Intros n p.
-Apply allnot with n; Auto.
+unfold not in |- *; intros P allnot exP; elim exP; intros n p.
+apply allnot with n; auto.
 Qed.
 
-End Generic.
+End Generic.
\ No newline at end of file