proposition: Lemma groupVr x : x \in G -> x^-1 \in G.
proof: Proof. move=> Gx; rewrite -(mul1g x^-1) -mem_rcoset ((G :* x =P G) _) //. by rewrite eqEcard card_rcoset leqnn mul_subG ?sub1set. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)