gros commit de tout ce que j'ai fait pendant les vacances :

 - tactics/Equality
 - debug du discharge
 - constr_of_compattern implante vite fait / mal fait en attendant mieux
 - theories/Logic (ne passe pas entierrement)


git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@280 85f007b7-540e-0410-9357-904b9bb8a0f7

1 files changed, 57 insertions, 0 deletions

diff --git a/theories/Logic/Classical_Pred_Type.v b/theories/Logic/Classical_Pred_Type.v
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+++ b/theories/Logic/Classical_Pred_Type.v
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+
+(* $Id$ *)
+
+(* Classical Predicate Logic on Type *)
+
+Require Classical_Prop.
+
+Section Generic.
+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)).
+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.
+Qed.
+
+Lemma not_all_not_ex : (P:U->Prop)(~(n:U)~(P n)) -> (EXT 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.
+Qed.
+
+Lemma not_ex_all_not : (P:U->Prop)(~(EXT n:U | (P n))) -> (n:U)~(P n).
+Proof.
+Unfold not; 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).
+Proof.
+Intros P H n.
+Apply NNPP.
+Red; 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).
+Proof.
+Unfold not; 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)).
+Proof.
+Unfold not; Intros P allnot exP; Elim exP; Intros n p.
+Apply allnot with n; Auto.
+Qed.
+
+End Generic.