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).