proposition: Lemma eq_mulgV1 x y : (x == y) = (x * y^-1 == 1 :> T).
proof: Proof. by rewrite -(inj_eq invg_inj) eq_invg_mul. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)