proposition: Lemma in_goto_spec_1_M {m i n X Y} : m < G -> In (i, (n, X, Y)) igotos -> In (goto_spec_1 m (i, (n, X, Y))) M.
proof: Proof. move=> ? ?. apply /in_app_r /in_app_r /in_app_l. rewrite -lock. apply /in_app_r /in_flat_map. exists m. constructor; [by apply /in_seq; lia | by apply /in_map]. 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