Definition axiom T (e : rel T) := forall x y, reflect (x = y) (e x y).Structure mixin_of T := Mixin {op : rel T; _ : axiom op}.Structure mixin_of T := Mixin {op : rel T; _ : axiom op}.Structure mixin_of T := Mixin {op : rel T; _ : axiom op}.Notation class_of := mixin_of (only parsing).Structure type := Pack {sort; _ : class_of sort; _ : Type}.Structure type := Pack {sort; _ : class_of sort; _ : Type}.Structure type := Pack {sort; _ : class_of sort; _ : Type}.Definition pack c := @Pack T c T.Notation eqTypeX := type.Notation EqMixinX := Mixin.Notation EqTypeX T m := (@pack T m).Definition eq_opX T := EqualityX.op (EqualityX.class T).

Lemma eqxP : Equality.axiom (@eq_opX U).