proposition: Lemma F_inv3 y : F O1 y -> y = O2.
proof: Proof. Proof using M2_correct M1_correct. destruct (case_analysis M2 M2_correct y) as [->|[y' ->]]. - easy. - now intros H%F_inv2. Qed.
imports: PeanoNat Lia Vector Undecidability.SOL(SOL PA2) Undecidability.Shared.Libs.PSL(Vectors) Undecidability.SOL.Util(Syntax Subst Tarski PA2_facts)