Require Import Undecidability.Synthetic.Undecidability.
Require Import Undecidability.StringRewriting.SR.
Require Import Undecidability.TM.SBTM_undec.
From Undecidability.StringRewriting.Reductions Require HaltSBTMu_to_SRH SRH_to_SR HaltSBTMu_to_TSR.
Lemma SRH_undec : undecidable SRH.
Proof.
apply (undecidability_from_reducibility HaltSBTMu_undec).
apply HaltSBTMu_to_SRH.reduction.
Qed.
Check SRH_undec.
Lemma SR_undec : undecidable SR.
Proof.
apply (undecidability_from_reducibility SRH_undec).
exact SRH_to_SR.reduction.
Qed.
Check SR_undec.
Lemma TSR_undec : undecidable TSR.
Proof.
apply (undecidability_from_reducibility HaltSBTMu_undec).
exact HaltSBTMu_to_TSR.reduction.
Qed.
Check SR_undec.