ExtLib.Core.EquivDec
From Coq.Classes Require Import EquivDec.
Theorem EquivDec_refl_left {T : Type} {c : EqDec T (@eq T)} :
forall (n : T), equiv_dec n n = left (refl_equal _).
Proof.
intros. destruct (equiv_dec n n); try congruence.
Require Eqdep_dec.
rewrite (Eqdep_dec.UIP_dec (A := T) (@equiv_dec _ _ _ c) e (refl_equal _)).
reflexivity.
Qed.
Export EquivDec.
Theorem EquivDec_refl_left {T : Type} {c : EqDec T (@eq T)} :
forall (n : T), equiv_dec n n = left (refl_equal _).
Proof.
intros. destruct (equiv_dec n n); try congruence.
Require Eqdep_dec.
rewrite (Eqdep_dec.UIP_dec (A := T) (@equiv_dec _ _ _ c) e (refl_equal _)).
reflexivity.
Qed.
Export EquivDec.