proposition: Lemma groupM x y : x \in G -> y \in G -> x * y \in G.
proof: Proof. by case/group_setP: (valP G) x y. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)