proposition: Lemma coset_invP : left_inverse coset_one coset_inv coset_mul.
proof: Proof. case=> B coB; apply: val_inj => /=; case/rcosetsP: coB => x Hx ->{B}. rewrite invg_rcoset -mulgA (mulgA H) mulGid. by rewrite norm_rlcoset ?nNH // -lcosetM mulVg mul1g. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq div) mathcomp(choice fintype prime finset fingroup morphism) mathcomp(automorphism)