Canonical Structure Map_setoid' : Setoid' := Ext_equiv'.Definition Map2' := Map' A (Map_setoid' 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).