Section maps''.
Variable A B : Setoid''.
Definition Map_law'' (f : A -> B) :=
forall x y : A, x =_S'' y -> f x =_S'' f y.
Structure > Map'' : Type :=  {Ap'' :> A -> B; Pres'' :> Map_law'' Ap''}.
(*** rewrite rule ***)
(* *)
Definition Ext'' (f g : Map'') := forall x : A, f x =_S'' g x.

Lemma Ext_equiv'' : Equivalence Ext''.