proposition: Lemma coprime_morph G H : coprime #|G| #|H| -> coprime #|f @* G| #|f @* H|.
proof: Proof. by move=> coGH; rewrite coprime_morphl // coprime_morphr. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq div) mathcomp(choice fintype prime finset fingroup morphism) mathcomp(automorphism)