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''}.Structure > Map'' : Type :=  {Ap'' :> A -> B; Pres'' :> Map_law'' Ap''}.Structure > Map'' : Type :=  {Ap'' :> A -> B; Pres'' :> Map_law'' Ap''}.

(* Specifications: *)
Lemma Pres1'' : forall (m : Map'') (x y : A), x =_S'' y -> m x =_S'' m y.