Variable f : {morphism G >-> rT}.
Hypothesis isoGH : isom G H f.

(* Specifications: *)
Lemma isom_inj : 'injm f. Proof. by have /isomP[] := isoGH. Qed.
Lemma isom_im : f @* G = H. Proof. by have /isomP[] := isoGH. Qed.
Lemma isom_card : #|G| = #|H|.
Lemma sub_isog (A : {set aT}) : A \subset G -> 'injm f -> isog A (f @* A).
Lemma isog_eq1 : G \isog H -> (G :==: 1) = (H :==: 1).
Lemma isog_symr : G \isog H -> H \isog G.
Lemma nclasses_isog : G \isog H -> #|classes G| = #|classes H|.
Lemma isog_transr : G \isog H -> (K \isog G) = (K \isog H).
End IsoBoolEquiv.