proposition: Fact vec_sum_is_zero n v : @vec_sum n v = 0 -> v = vec_zero.
proof: Proof. induction v as [ | n x v IHv ]; simpl; auto. simpl; rewrite vec_zero_S; intros; f_equal. + lia. + apply IHv; lia. Qed.
imports: Arith Lia List Permutation Undecidability.Shared.Libs.DLW.Utils(utils) Undecidability.Shared.Libs.DLW.Vec(pos)