proposition: Fact fo_term_subst_comp t : t⟬f⟭ ⟬g⟭ = t⟬fun x => (f x)⟬g⟭ ⟭ .
proof: Proof. induction t; simpl; auto. rewrite vec_map_map; f_equal. apply vec_pos_ext; intros p; rew vec. Qed.
imports: List Arith Lia Eqdep_dec Undecidability.Shared.Libs.DLW.Utils(utils_tac utils_list utils_nat finite) Undecidability.Shared.Libs.DLW.Vec(pos vec) Undecidability.FOL.TRAKHTENBROT(notations utils decidable fol_ops fo_sig)