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| author |  herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2006-06-04 17:59:53 +0000 |
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| committer | herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2006-06-04 17:59:53 +0000 |
| commit | 03c392f24a204be29093166b9c42fa5c485e627c (patch) | |
| tree | ab7a5404f12e452ded8742b7a026d6cfad92b374 /theories/Logic/Classical_Prop.v | |
| parent | f288a7f38b1ad0b6e9ab6d01ea6cded80cc867c6 (diff) | |
Ajout exists! et restructuration/extension des fichiers sur la
description et le choix
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@8892 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Logic/Classical_Prop.v')
| -rw-r--r-- | theories/Logic/Classical_Prop.v | 9 |
1 files changed, 9 insertions, 0 deletions
diff --git a/theories/Logic/Classical_Prop.v b/theories/Logic/Classical_Prop.v index d714b3bf7..8d2e946de 100644 --- a/theories/Logic/Classical_Prop.v +++ b/theories/Logic/Classical_Prop.v @@ -22,6 +22,15 @@ unfold not in |- *; intros; elim (classic p); auto. intro NP; elim (H NP). Qed. +(** Peirce's law states [forall P Q:Prop, ((P -> Q) -> P) -> P]. + Thanks to [forall P, False -> P], it is equivalent to the + following form *) + +Lemma Peirce : forall P:Prop, ((P -> False) -> P) -> P. +Proof. +intros P H; destruct (classic P); auto. +Qed. + Lemma not_imply_elim : forall P Q:Prop, ~ (P -> Q) -> P. Proof. intros; apply NNPP; red in |- *. |