Infix "\isog" := isog.
Arguments isom_isog [A B D].
(* The real reflection properties only hold for true groups and morphisms. *)
Section Main.
Variables (G : {group aT}) (H : {group rT}).

(* Specifications: *)
Lemma isomP (f : {morphism G >-> rT}) :
reflect ('injm f /\ f @* G = H) (isom G H f).
Lemma isogP :
reflect (exists2 f : {morphism G >-> rT}, 'injm f & f @* G = H) (G \isog H).