Require Import Undecidability.Synthetic.Undecidability.

From Undecidability.StackMachines Require Import BSM BSM_undec.
From Undecidability.MinskyMachines Require Import MM Reductions.BSM_MM.

Lemma MM_HALTS_ON_ZERO_undec : undecidable MM_HALTS_ON_ZERO.
Proof.
  apply (undecidability_from_reducibility BSM_undec).
  apply BSM_MM_HALTS_ON_ZERO.
Qed.

Lemma MM_HALTING_undec : undecidable MM_HALTING.
Proof.
  apply (undecidability_from_reducibility BSM_undec).
  apply BSM_MM_HALTING.
Qed.

Lemma MM_HALTING_compl_undec : mundecidable (complement MM_HALTING).
Proof.
  apply (mundecidability_from_reducibility BSM_compl_undec).
  apply reduces_complement.
  apply BSM_MM_HALTING.
Qed.