TypeWithRelation -> TypeWithRelation -> Type := fun '(A; R__A) '(B; R__B) => { f : A <~> B & forall a a', R__A a a' <-> R__B (f a) (f a') }. Global Instance isomorphism_id : Reflexive . Proof. intros A. exists equiv_idmap. cbn. intros a a'. reflexivity. Qed.
From HoTT Require Import TruncType ExcludedMiddle Modalities.ReflectiveSubuniverse abstract_algebra. From HoTT Require Import Universes.Smallness. From HoTT Require Import Colimits.Quotient. From HoTT Require Import HSet.