Definition surj_group_quo_ker :
  Hom G (group_quo G (Ker f) (kernel_normal (G:=G) (G':=G') (f:=f))) :=
  group_quo_surj (kernel_normal (f:=f)).

(* Specifications: *)
Lemma surj_group_quo_ker_surjective : surjective surj_group_quo_ker.