From mathcomp.ssreflect
From mathcomp
Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.
(* We need a custom equality type, as the default one from ssreflect breaks constraint solving when defining worlds.  TODO: figure out, why? *)
Module EqualityX.
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}.
Notation class_of := mixin_of (only parsing).
Section ClassDef.
Structure type := Pack {sort; _ : class_of sort; _ : Type}.
Local Coercion sort : type >-> Sortclass.
Variables (T : Type) (cT : type).
Definition class := let: Pack _ c _ := cT return class_of cT in c.
Definition pack c := @Pack T c T.
Definition clone := fun c & cT -> T & phant_id (pack c) cT => pack c.
End ClassDef.
Module Exports.
Coercion sort : type >-> Sortclass.
Notation eqTypeX := type.
Notation EqMixinX := Mixin.
Notation EqTypeX T m := (@pack T m).
End Exports.
End EqualityX.
Export EqualityX.Exports.
Section EqualityConversion.
Variable U: eqTypeX.
Definition eq_opX T := EqualityX.op (EqualityX.class T).

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