proposition: Lemma rcoset_id x : x \in G -> G :* x = G.
proof: Proof. by move=> Gx; rewrite (rcoset_eqP (_ : x \in G :* 1)) mulg1. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)