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.