Implicit Types rT gT aT : finGroupType.

(* Specifications: *)
Lemma homg_refl aT (A : {set aT}) : homg A A.
Lemma homg_trans aT (B : {set aT}) rT (C : {set rT}) gT (G : {group gT}) : homg C B -> homg B G -> homg C G.
Lemma isog_hom rT aT (G : {group rT}) (H : {group aT}) : G \isog H -> homg G H.
Lemma isogEhom rT aT (G : {group rT}) (H : {group aT}) : (G \isog H) = homg G H && homg H G.
Lemma eq_homgl gT aT rT (G : {group gT}) (H : {group aT}) (K : {group rT}) : G \isog H -> homg G K = homg H K.
Lemma eq_homgr gT rT aT (G : {group gT}) (H : {group rT}) (K : {group aT}) : G \isog H -> homg K G = homg K H.