proposition: Lemma in_igotos_unique {i n X Y n' X' Y'} : In (i, (n, X, Y)) igotos -> In (i, (n', X', Y')) igotos -> n = n' /\ X = X' /\ Y = Y'.
proof: Proof. move=> /nth_error_Some_In_combineP + /nth_error_Some_In_combineP => -> [] *. by subst. 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