proposition: Lemma eq_invg_mul x y : (x^-1 == y :> T) = (x * y == 1 :> T).
proof: Proof. by rewrite -(inj_eq (@mulgI x)) mulgV eq_sym. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)