proposition: Lemma in_index_yes_spec_1_M {i j n} : In (i, (j, n)) iP -> In (index_yes_spec_1 (i, (j, n))) M.
proof: Proof. move=> ?. rewrite /M -[locked index_ops]lock. apply /in_app_l /in_app_r /in_app_r /in_app_l /in_map_iff. by eexists. 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