proposition: Lemma not_in_iPI {i x} : length P <= i -> not (In (i, x) iP).
proof: Proof. move=> ? /in_combine_l /in_seq. by lia. Qed.
imports: Relation_Operators Operators_Properties Lia PeanoNat List Undecidability.StackMachines.Reductions.CM1_HALT_to_SMNdl_UB.SMX_facts Undecidability.StackMachines.Util(Nat_facts List_facts) ssreflect ssrbool ssrfun