Definition group_quo_ker := group_quo G Ker kernel_normal.

(* Specifications: *)
Lemma Ker_prop : forall x : G, in_part x Ker -> Equal (f x) (monoid_unit G').
Lemma Ker_prop_rev : forall x : G, Equal (f x) (monoid_unit G') -> in_part x Ker.
Lemma coKer_prop : forall x : G, in_part (f x) coKer.