Definition Map2_alt := Map (SPROD A B) C.Definition Map2_congl_law :=
  forall (b1 b2 : B) (a : A), b1 =_S b2 -> f a b1 =_S f a b2.Definition Map2_congr_law :=
  forall (a1 a2 : A) (b : B), a1 =_S a2 -> f a1 b =_S f a2 b.Definition Map2_cong_law :=
  forall (a1 a2 : A) (b1 b2 : B),
  a1 =_S a2 -> b1 =_S b2 -> f a1 b1 =_S f a2 b2.

(* Specifications: *)
Lemma Map2_map_law1 : forall a : A, Map_law (f a).