proposition: Lemma Ack_not_PR : False.
proof: Proof. destruct (majorPR2_strict Ack HAck) as [m Hm]. set (x := Nat.max 2 m). specialize (Hm x x); rewrite Nat.max_idempotent in Hm. assert (H0: Ack m x <= Ack x x) by (apply Ack_mono_l; lia). lia. Qed.
imports: hydras(primRec Ack MoreVectors) Coq(Arith ArithRing List Lia Compare_dec)