proposition: Lemma iso_vec_eq1 ar (v1 v1' : vec D1 ar) v2 : v1 ≈ v2 -> v1' ≈ v2 -> v1 = v1'.
proof: Proof. Proof using M2_correct M1_correct. intros H1 H2. induction v1 as [|? n ? IHv1]. - pattern v1'. now apply Vector.case0. - revert H2. apply (Vector.caseS' v1'). intros. f_equal. eapply F_injective. apply H1. apply H2. eapply IHv1. apply H1. apply H2. Qed.
imports: PeanoNat Lia Vector Undecidability.SOL(SOL PA2) Undecidability.Shared.Libs.PSL(Vectors) Undecidability.SOL.Util(Syntax Subst Tarski PA2_facts)