proposition: Lemma in_scan_gotos {i j n} : In (i, (j, n)) iP -> In (n, #+i, #-i) gotos.
proof: Proof. move=> ?. apply /in_app_l /in_map_iff. eexists. by constructor; last by eassumption. 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