(* 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_morphpre L M :
L \subset f @* D -> #|f @*^-1 L : f @*^-1 M| = #|L : M|.