proposition: Lemma in_iPI {i} : i < length P -> exists j n, In (i, (j, n)) iP.
proof: Proof. move H: (nth_error P i) => x ?. case: x H; last by (move /nth_error_None; lia). move=> [j n] /nth_error_Some_In_iP ?. by exists j, n. 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