fact: Fixpoint Σ2_is_tuple t n : vec nat n -> fol_form Σ2 := match n with | 0 => fun _ => ∀ 0 ∈ (S t) ⤑ ⊥ | S n => fun v => ∃ Σ2_is_opair (S t) (S (vec_head v)) 0 ⟑ Σ2_is_tuple 0 (vec_map S (vec_tail v)) end.
imports: List Arith Nat Lia Max Wellfounded Coq.Setoids.Setoid Undecidability.Shared.Libs.DLW.Utils(utils_tac utils_list finite) Undecidability.Shared.Libs.DLW.Vec(pos vec) Undecidability.FOL.TRAKHTENBROT(notations fol_ops fo_sig fo_terms fo_logic)