Section Def.
Variable G G' : GROUP.
Variable f : Hom G G'.
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)).

Lemma surj_group_quo_ker_surjective : surjective surj_group_quo_ker.