proposition: Theorem is_inv_aux_false: forall b l, (forall a, (In a l) -> op b a <> e \/ op a b <> e) -> is_inv_aux l b = false.
proof: Proof. intros b l; elim l; simpl; auto. intros a l1 Rec H; case (A_dec (op a b) e); case (A_dec (op b a) e); auto. intros H1 H2; case (H a); auto; intros H3; case H3; auto. Qed.
imports: ZArith Tactic Wf_nat UList ListAux FGroup