(* Counting lemmas for morphisms. *)
Section CardMorphism.
Variables (aT rT : finGroupType) (D : {group aT}) (f : {morphism D >-> rT}).
Implicit Types G H : {group aT}.
Implicit Types L M : {group rT}.

Lemma card_morphim G : #|f @* G| = #|D :&: G : 'ker f|.