From 619ab2496a3872cdda1b8f480dc79aa71fa4ae1d Mon Sep 17 00:00:00 2001 From: Jason Gross Date: Mon, 7 Nov 2016 14:49:38 -0500 Subject: Add IffT, some Proper prod lemmas --- src/Util/IffT.v | 9 +++++++++ 1 file changed, 9 insertions(+) create mode 100644 src/Util/IffT.v (limited to 'src/Util/IffT.v') diff --git a/src/Util/IffT.v b/src/Util/IffT.v new file mode 100644 index 000000000..fd132fbfa --- /dev/null +++ b/src/Util/IffT.v @@ -0,0 +1,9 @@ +Require Import Coq.Classes.RelationClasses. +Notation iffT := (fun A B => inhabited ((A -> B) * (B -> A)))%type. + +Global Instance iffT_Reflexive : Reflexive iffT | 1. +Proof. repeat constructor; intro; assumption. Defined. +Global Instance iffT_Symmetric : Symmetric iffT | 1. +Proof. repeat (intros [?] || intro); constructor; tauto. Defined. +Global Instance iffT_Transitive : Transitive iffT | 1. +Proof. repeat (intros [?] || intro); constructor; tauto. Defined. -- cgit v1.2.3