proposition: Lemma F_inv2 y : F O1 (S2 y) -> False.
proof: Proof. Proof using M2_correct M1_correct. intros H. inversion H. + now apply (zero_succ M2 M2_correct y). + now apply (zero_succ M1 M1_correct x). Qed.
imports: PeanoNat Lia Vector Undecidability.SOL(SOL PA2) Undecidability.Shared.Libs.PSL(Vectors) Undecidability.SOL.Util(Syntax Subst Tarski PA2_facts)