diff options
Diffstat (limited to 'theories/Numbers/Integer/TreeMod/ZTreeMod.v')
| -rw-r--r-- | theories/Numbers/Integer/TreeMod/ZTreeMod.v | 22 |
1 files changed, 17 insertions, 5 deletions
diff --git a/theories/Numbers/Integer/TreeMod/ZTreeMod.v b/theories/Numbers/Integer/TreeMod/ZTreeMod.v index 7ee894ca4c..75e9c9f77e 100644 --- a/theories/Numbers/Integer/TreeMod/ZTreeMod.v +++ b/theories/Numbers/Integer/TreeMod/ZTreeMod.v @@ -1,3 +1,15 @@ +(************************************************************************) +(* 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 *) +(************************************************************************) +(* Evgeny Makarov, INRIA, 2007 *) +(************************************************************************) + +(*i i*) + Require Export NZAxioms. Require Import NMake. (* contains W0Type *) Require Import ZnZ. @@ -24,17 +36,17 @@ Definition NZplus := w_op.(znz_add). Definition NZminus := w_op.(znz_sub). Definition NZtimes := w_op.(znz_mul). -Theorem NZE_equiv : equiv NZ NZeq. +Theorem NZeq_equiv : equiv NZ NZeq. Proof. unfold equiv, reflexive, symmetric, transitive, NZeq; repeat split; intros; auto. now transitivity [| y |]. Qed. Add Relation NZ NZeq - reflexivity proved by (proj1 NZE_equiv) - symmetry proved by (proj2 (proj2 NZE_equiv)) - transitivity proved by (proj1 (proj2 NZE_equiv)) -as NZE_rel. + reflexivity proved by (proj1 NZeq_equiv) + symmetry proved by (proj2 (proj2 NZeq_equiv)) + transitivity proved by (proj1 (proj2 NZeq_equiv)) +as NZeq_rel. Add Morphism NZsucc with signature NZeq ==> NZeq as NZsucc_wd. Proof. |