fact: Fixpoint fo_term_rect t : P t := match t with | in_var x => HP0 x | in_fot v => IHP v (fun p => fo_term_rect (vec_pos v p)) end.
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)