proposition: Lemma groupMr x y : x \in G -> (y * x \in G) = (y \in G).
proof: Proof. by move=> Gx; rewrite -[_ \in G]groupV invMg groupMl groupV. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)