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authorherbelin2005-12-26 13:59:13 +0000
committerherbelin2005-12-26 13:59:13 +0000
commitf6e1acbbe00aeb479fde229c3941e3a6a2d53068 (patch)
treece3a6476de30cbf68c7668f5ecba92f457a721e8 /theories7/Wellfounded/Inverse_Image.v
parente0f9487be5ce770117a9c9c815af8c7010ff357b (diff)
Suppression des fichiers .v en ancienne syntaxe
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-(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
-(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(************************************************************************)
-
-(*i $Id$ i*)
-
-(** Author: Bruno Barras *)
-
-Section Inverse_Image.
-
- Variables A,B:Set.
- Variable R : B->B->Prop.
- Variable f:A->B.
-
- Local Rof : A->A->Prop := [x,y:A](R (f x) (f y)).
-
- Remark Acc_lemma : (y:B)(Acc B R y)->(x:A)(y=(f x))->(Acc A Rof x).
- NewInduction 1 as [y _ IHAcc]; Intros x H.
- Apply Acc_intro; Intros y0 H1.
- Apply (IHAcc (f y0)); Try Trivial.
- Rewrite H; Trivial.
- Qed.
-
- Lemma Acc_inverse_image : (x:A)(Acc B R (f x)) -> (Acc A Rof x).
- Intros; Apply (Acc_lemma (f x)); Trivial.
- Qed.
-
- Theorem wf_inverse_image: (well_founded B R)->(well_founded A Rof).
- Red; Intros; Apply Acc_inverse_image; Auto.
- Qed.
-
- Variable F : A -> B -> Prop.
- Local RoF : A -> A -> Prop := [x,y]
- (EX b : B | (F x b) & (c:B)(F y c)->(R b c)).
-
-Lemma Acc_inverse_rel :
- (b:B)(Acc B R b)->(x:A)(F x b)->(Acc A RoF x).
-NewInduction 1 as [x _ IHAcc]; Intros x0 H2.
-Constructor; Intros y H3.
-NewDestruct H3.
-Apply (IHAcc x1); Auto.
-Save.
-
-
-Theorem wf_inverse_rel :
- (well_founded B R)->(well_founded A RoF).
- Red; Constructor; Intros.
- Case H0; Intros.
- Apply (Acc_inverse_rel x); Auto.
-Save.
-
-End Inverse_Image.
-
-