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