(* 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_morphpre L : L \subset f @* D -> #|f @*^-1 L| = (#|'ker f| * #|L|)%N.