proposition: Lemma sub_cfker_morph phi (A : {set aT}) : (A \subset cfker (cfMorph phi)) = (A \subset G) && (f @* A \subset cfker phi).
proof: Proof. rewrite cfker_morph // subsetI; apply: andb_id2l => sAG. by rewrite sub_morphim_pre // (subset_trans sAG). Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div choice fintype tuple finfun bigop prime order) mathcomp(ssralg poly finset fingroup morphism perm) mathcomp(automorphism quotient finalg action gproduct) mathcomp(zmodp commutator cyclic center pgroup sylow) mathcomp(matrix vector falgebra ssrnum algC algnum) mathcomp(archimedean)