Notation "x \isog y":= (isog x y).Definition isom_inv := restrm isom_sub_im (invm isom_inj).

(* Specifications: *)
Lemma idm_isom : isom G G (idm G).
Lemma isog_refl : G \isog G.
Lemma isog_abelian : G \isog H -> abelian G = abelian H.
Lemma isog_symr : G \isog H -> H \isog G.
Lemma isog_trans : G \isog H -> H \isog K -> G \isog K.
Lemma isog_sym : (G \isog H) = (H \isog G).
Lemma isog_transl : G \isog H -> (G \isog K) = (H \isog K).
Lemma isog_transr : G \isog H -> (K \isog G) = (K \isog H).