proposition: Lemma val_coset_prim x : x \in 'N(A) -> coset x :=: H :* x.
proof: Proof. by move=> Nx; rewrite val_insubd /= mem_rcosets -{1}(mul1g x) mem_mulg. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq div) mathcomp(choice fintype prime finset fingroup morphism) mathcomp(automorphism)