proposition: Lemma coset_oneP : left_id coset_one coset_mul.
proof: Proof. case=> B coB; apply: val_inj => /=; case/rcosetsP: coB => x Hx ->{B}. by rewrite mulgA mulGid. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq div) mathcomp(choice fintype prime finset fingroup morphism) mathcomp(automorphism)