From 03e2f7a1bf6ee15608aceb455e0c30a2780eff56 Mon Sep 17 00:00:00 2001 From: herbelin Date: Sun, 5 Dec 2004 16:44:57 +0000 Subject: MAJ changements ChoiceFacts git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@6401 85f007b7-540e-0410-9357-904b9bb8a0f7 --- theories/Logic/ClassicalChoice.v | 9 +++++---- theories/Logic/Diaconescu.v | 8 ++++---- 2 files changed, 9 insertions(+), 8 deletions(-) (limited to 'theories') diff --git a/theories/Logic/ClassicalChoice.v b/theories/Logic/ClassicalChoice.v index 0bc491e20..69887a540 100644 --- a/theories/Logic/ClassicalChoice.v +++ b/theories/Logic/ClassicalChoice.v @@ -23,10 +23,11 @@ Require Import ChoiceFacts. Theorem choice : forall (A B:Type) (R:A -> B -> Prop), - (forall x:A, exists y : B, R x y) -> + (forall x:A, exists y : B, R x y) -> exists f : A -> B, (forall x:A, R x (f x)). Proof. +intros A B. apply description_rel_choice_imp_funct_choice. -exact description. -exact relational_choice. -Qed. \ No newline at end of file +exact (description A B). +exact (relational_choice A B). +Qed. diff --git a/theories/Logic/Diaconescu.v b/theories/Logic/Diaconescu.v index d815b9dda..5f7112fd7 100644 --- a/theories/Logic/Diaconescu.v +++ b/theories/Logic/Diaconescu.v @@ -59,18 +59,18 @@ Qed. Require Import ChoiceFacts. -Variable rel_choice : RelationalChoice. +Variable rel_choice : forall A B:Type, RelationalChoice A B. Lemma guarded_rel_choice : forall (A B:Type) (P:A -> Prop) (R:A -> B -> Prop), (forall x:A, P x -> exists y : B, R x y) -> - exists R' : A -> B -> Prop, + exists R' : A -> B -> Prop, (forall x:A, P x -> exists y : B, R x y /\ R' x y /\ (forall y':B, R' x y' -> y = y')). Proof. - exact - (rel_choice_and_proof_irrel_imp_guarded_rel_choice rel_choice proof_irrel). + apply + (rel_choice_and_proof_irrel_imp_guarded_rel_choice rel_choice proof_irrel). Qed. (** The form of choice we need: there is a functional relation which chooses -- cgit v1.2.3