proposition: Lemma zero_prefix_lt {n m v w} : §0^n ++ [§1] ++ v = §0^m ++ w -> m <= n.
proof: Proof. elim: m n; first by lia. move=> m IH [|n]; first done. have H : forall k, §0^(S k) = [§0] ++ §0^k by (move=> ?; rewrite ?app_norm). rewrite ?H -?app_assoc. move /app_inv_head /IH. by lia. 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