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Diffstat (limited to 'theories/Classes/Functions.v')
| -rw-r--r-- | theories/Classes/Functions.v | 41 |
1 files changed, 0 insertions, 41 deletions
diff --git a/theories/Classes/Functions.v b/theories/Classes/Functions.v deleted file mode 100644 index 998f8cb7..00000000 --- a/theories/Classes/Functions.v +++ /dev/null @@ -1,41 +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 *) -(************************************************************************) - -(* Functional morphisms. - - Author: Matthieu Sozeau - Institution: LRI, CNRS UMR 8623 - UniversitĂcopyright Paris Sud - 91405 Orsay, France *) - -(* $Id: Functions.v 11709 2008-12-20 11:42:15Z msozeau $ *) - -Require Import Coq.Classes.RelationClasses. -Require Import Coq.Classes.Morphisms. - -Set Implicit Arguments. -Unset Strict Implicit. - -Class Injective `(m : Morphism (A -> B) (RA ++> RB) f) : Prop := - injective : forall x y : A, RB (f x) (f y) -> RA x y. - -Class Surjective `(m : Morphism (A -> B) (RA ++> RB) f) : Prop := - surjective : forall y, exists x : A, RB y (f x). - -Definition Bijective `(m : Morphism (A -> B) (RA ++> RB) (f : A -> B)) := - Injective m /\ Surjective m. - -Class MonoMorphism `(m : Morphism (A -> B) (eqA ++> eqB)) := - monic :> Injective m. - -Class EpiMorphism `(m : Morphism (A -> B) (eqA ++> eqB)) := - epic :> Surjective m. - -Class IsoMorphism `(m : Morphism (A -> B) (eqA ++> eqB)) := - { monomorphism :> MonoMorphism m ; epimorphism :> EpiMorphism m }. - -Class AutoMorphism `(m : Morphism (A -> A) (eqA ++> eqA)) {I : IsoMorphism m}. |