proposition: Lemma nth_error_Some_In_iP {i j n} : nth_error P i = Some (j, n) <-> In (i, (j, n)) iP.
proof: Proof. by apply: nth_error_Some_In_combineP. 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