(* 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 index_morphim G H : G :&: H \subset D -> #|f @* G : f @* H| %| #|G : H|.