proposition: Lemma cosetpre_maximal (Q R : {group coset_of K}) : maximal (coset K @*^-1 Q) (coset K @*^-1 R) = maximal Q R.
proof: Proof. by rewrite morphpre_maximal ?sub_im_coset. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(fintype bigop finset fingroup morphism) mathcomp(automorphism quotient action commutator center)