diff options
author | barras <barras@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2003-12-15 19:48:24 +0000 |
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committer | barras <barras@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2003-12-15 19:48:24 +0000 |
commit | 3675bac6c38e0a26516e434be08bc100865b339b (patch) | |
tree | 87f8eb1905c7b508dea60b1e216f79120e9e772d /theories/Logic/ClassicalDescription.v | |
parent | c881bc37b91a201f7555ee021ccb74adb360d131 (diff) |
modif existentielle (exists | --> exists ,) + bug d'affichage des pt fixes
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@5099 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Logic/ClassicalDescription.v')
-rw-r--r-- | theories/Logic/ClassicalDescription.v | 10 |
1 files changed, 5 insertions, 5 deletions
diff --git a/theories/Logic/ClassicalDescription.v b/theories/Logic/ClassicalDescription.v index 26e696a7c..a20036f0a 100644 --- a/theories/Logic/ClassicalDescription.v +++ b/theories/Logic/ClassicalDescription.v @@ -26,15 +26,15 @@ Axiom dependent_description : forall (A:Type) (B:A -> Type) (R:forall x:A, B x -> Prop), (forall x:A, - exists y : B x | R x y /\ (forall y':B x, R x y' -> y = y')) -> - exists f : forall x:A, B x | (forall x:A, R x (f x)). + exists y : B x, R x y /\ (forall y':B x, R x y' -> y = y')) -> + exists f : forall x:A, B x, (forall x:A, R x (f x)). (** Principle of definite description (aka axiom of unique choice) *) Theorem description : forall (A B:Type) (R:A -> B -> Prop), - (forall x:A, exists y : B | R x y /\ (forall y':B, R x y' -> y = y')) -> - exists f : A -> B | (forall x:A, R x (f x)). + (forall x:A, exists y : B, R x y /\ (forall y':B, R x y' -> y = y')) -> + exists f : A -> B, (forall x:A, R x (f x)). Proof. intros A B. apply (dependent_description A (fun _ => B)). @@ -46,7 +46,7 @@ Theorem classic_set : ((forall P:Prop, {P} + {~ P}) -> False) -> False. Proof. intro HnotEM. pose (R := fun A b => A /\ true = b \/ ~ A /\ false = b). -assert (H : exists f : Prop -> bool | (forall A:Prop, R A (f A))). +assert (H : exists f : Prop -> bool, (forall A:Prop, R A (f A))). apply description. intro A. destruct (classic A) as [Ha| Hnota]. |