Definition func_absgp (A : Setoid) (B : abelian_sgroup) : ABELIAN_SGROUP :=
  Build_abelian_sgroup
    (Build_abelian_sgroup_on (A:=func_sgroup A B)
       (func_plus_commutative (A:=A) (B:=B))).Definition func_zerofun : forall (A : Setoid) (B : monoid), func_set A B.

Lemma func_zerofun_is_r_unit : forall (A : Setoid) (B : monoid), unit_r (sgroup_law_map (func_sgroup A B)) (func_zerofun A B).