H10UPC_SAT is undecidable

Require Import Undecidability.Synthetic.Undecidability.

Require Import Undecidability.DiophantineConstraints.H10UPC.

From Undecidability.DiophantineConstraints Require Import H10C H10C_undec.
From Undecidability.DiophantineConstraints.Reductions Require H10UC_SAT_to_H10UPC_SAT.

Theorem H10UPC_SAT_undec : undecidable H10UPC_SAT.
Proof.
  apply (undecidability_from_reducibility H10UC_SAT_undec).
  exact H10UC_SAT_to_H10UPC_SAT.reduction.
Qed.

Theorem H10UPC_SAT_compl_undec : mundecidable (complement H10UPC_SAT).
Proof.
  apply (mundecidability_from_reducibility H10UC_SAT_compl_undec).
  apply reduces_complement.
  exact H10UC_SAT_to_H10UPC_SAT.reduction.
Qed.