diff options
author | Samuel Mimram <smimram@debian.org> | 2006-04-28 14:59:16 +0000 |
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committer | Samuel Mimram <smimram@debian.org> | 2006-04-28 14:59:16 +0000 |
commit | 3ef7797ef6fc605dfafb32523261fe1b023aeecb (patch) | |
tree | ad89c6bb57ceee608fcba2bb3435b74e0f57919e /theories7/Wellfounded/Well_Ordering.v | |
parent | 018ee3b0c2be79eb81b1f65c3f3fa142d24129c8 (diff) |
Imported Upstream version 8.0pl3+8.1alphaupstream/8.0pl3+8.1alpha
Diffstat (limited to 'theories7/Wellfounded/Well_Ordering.v')
-rw-r--r-- | theories7/Wellfounded/Well_Ordering.v | 72 |
1 files changed, 0 insertions, 72 deletions
diff --git a/theories7/Wellfounded/Well_Ordering.v b/theories7/Wellfounded/Well_Ordering.v deleted file mode 100644 index 5c2b2405..00000000 --- a/theories7/Wellfounded/Well_Ordering.v +++ /dev/null @@ -1,72 +0,0 @@ -(************************************************************************) -(* 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: Well_Ordering.v,v 1.1.2.1 2004/07/16 19:31:42 herbelin Exp $ i*) - -(** Author: Cristina Cornes. - From: Constructing Recursion Operators in Type Theory - L. Paulson JSC (1986) 2, 325-355 *) - -Require Eqdep. - -Section WellOrdering. -Variable A:Set. -Variable B:A->Set. - -Inductive WO : Set := - sup : (a:A)(f:(B a)->WO)WO. - - -Inductive le_WO : WO->WO->Prop := - le_sup : (a:A)(f:(B a)->WO)(v:(B a)) (le_WO (f v) (sup a f)). - - -Theorem wf_WO : (well_founded WO le_WO ). -Proof. - Unfold well_founded ;Intro. - Apply Acc_intro. - Elim a. - Intros. - Inversion H0. - Apply Acc_intro. - Generalize H4 ;Generalize H1 ;Generalize f0 ;Generalize v. - Rewrite -> H3. - Intros. - Apply (H v0 y0). - Cut (eq ? f f1). - Intros E;Rewrite -> E;Auto. - Symmetry. - Apply (inj_pair2 A [a0:A](B a0)->WO a0 f1 f H5). -Qed. - -End WellOrdering. - - -Section Characterisation_wf_relations. - -(** Wellfounded relations are the inverse image of wellordering types *) -(* in course of development *) - - -Variable A:Set. -Variable leA:A->A->Prop. - -Definition B:= [a:A] {x:A | (leA x a)}. - -Definition wof: (well_founded A leA)-> A-> (WO A B). -Proof. - Intros. - Apply (well_founded_induction A leA H [a:A](WO A B));Auto. - Intros. - Apply (sup A B x). - Unfold 1 B . - NewDestruct 1 as [x0]. - Apply (H1 x0);Auto. -Qed. - -End Characterisation_wf_relations. |