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Diffstat (limited to 'src/Util/IffT.v')
| -rw-r--r-- | src/Util/IffT.v | 10 |
1 files changed, 10 insertions, 0 deletions
diff --git a/src/Util/IffT.v b/src/Util/IffT.v new file mode 100644 index 000000000..f4eaa9d53 --- /dev/null +++ b/src/Util/IffT.v @@ -0,0 +1,10 @@ +Require Import Coq.Classes.RelationClasses. +Notation iffT A B := (((A -> B) * (B -> A)))%type. +Notation iffTp := (fun A B => inhabited (iffT A B)). + +Global Instance iffTp_Reflexive : Reflexive iffTp | 1. +Proof. repeat constructor; intro; assumption. Defined. +Global Instance iffTp_Symmetric : Symmetric iffTp | 1. +Proof. repeat (intros [?] || intro); constructor; tauto. Defined. +Global Instance iffTp_Transitive : Transitive iffTp | 1. +Proof. repeat (intros [?] || intro); constructor; tauto. Defined. |