proposition: Lemma ack_add_bound2 i j k (H: i < ack(k,j)): i + j < ack (4 + k, j).
proof: Proof. replace (4 + k) with (4 + k + 0) by apply add_0_r. eapply lt_trans. 2: apply (ack_add_bound k 0 j). rewrite ack_equation_1. apply add_lt_mono. - exact H. - apply lt_succ_diag_r. Qed.
imports: Arith Lia Equations(Equations)