diff options
author | Samuel Mimram <smimram@debian.org> | 2008-07-25 15:12:53 +0200 |
---|---|---|
committer | Samuel Mimram <smimram@debian.org> | 2008-07-25 15:12:53 +0200 |
commit | a0cfa4f118023d35b767a999d5a2ac4b082857b4 (patch) | |
tree | dabcac548e299fee1da464c93b3dba98484f45b1 /theories/Setoids/Setoid_Prop.v | |
parent | 2281410e38ef99d025ea77194585a9bc019fdaa9 (diff) |
Imported Upstream version 8.2~beta3+dfsgupstream/8.2.beta3+dfsg
Diffstat (limited to 'theories/Setoids/Setoid_Prop.v')
-rw-r--r-- | theories/Setoids/Setoid_Prop.v | 79 |
1 files changed, 79 insertions, 0 deletions
diff --git a/theories/Setoids/Setoid_Prop.v b/theories/Setoids/Setoid_Prop.v new file mode 100644 index 00000000..7300937e --- /dev/null +++ b/theories/Setoids/Setoid_Prop.v @@ -0,0 +1,79 @@ + +(************************************************************************) +(* 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: Setoid_Prop.v 10739 2008-04-01 14:45:20Z herbelin $: i*) + +Require Import Setoid_tac. + +(** * A few examples on [iff] *) + +(** [iff] as a relation *) + +Add Relation Prop iff + reflexivity proved by iff_refl + symmetry proved by iff_sym + transitivity proved by iff_trans +as iff_relation. + +(** [impl] as a relation *) + +Theorem impl_trans: transitive _ impl. +Proof. + hnf; unfold impl; tauto. +Qed. + +Add Relation Prop impl + reflexivity proved by impl_refl + transitivity proved by impl_trans +as impl_relation. + +(** [impl] is a morphism *) + +Add Morphism impl with signature iff ==> iff ==> iff as Impl_Morphism. +Proof. + unfold impl; tauto. +Qed. + +(** [and] is a morphism *) + +Add Morphism and with signature iff ==> iff ==> iff as And_Morphism. + tauto. +Qed. + +(** [or] is a morphism *) + +Add Morphism or with signature iff ==> iff ==> iff as Or_Morphism. +Proof. + tauto. +Qed. + +(** [not] is a morphism *) + +Add Morphism not with signature iff ==> iff as Not_Morphism. +Proof. + tauto. +Qed. + +(** The same examples on [impl] *) + +Add Morphism and with signature impl ++> impl ++> impl as And_Morphism2. +Proof. + unfold impl; tauto. +Qed. + +Add Morphism or with signature impl ++> impl ++> impl as Or_Morphism2. +Proof. + unfold impl; tauto. +Qed. + +Add Morphism not with signature impl --> impl as Not_Morphism2. +Proof. + unfold impl; tauto. +Qed. + |