Section Homg.
Implicit Types rT gT aT : finGroupType.
Definition homg rT aT (C : {set rT}) (D : {set aT}) :=
[exists (f : {ffun aT -> rT} | morphic D f), f @: D == C].

Lemma isogEcard rT aT (G : {group rT}) (H : {group aT}) :
(G \isog H) = (homg G H) && (#|H| <= #|G|).