Section Main.
Variables (G : {group aT}) (H : {group rT}).
Variable f : {morphism G >-> rT}.
Hypothesis isoGH : isom G H f.

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|.