File size: 976 Bytes
37bcf52 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | import OAI.MathematicalPhysics.NavierStokes.ForcedComputation.Programs.FixedInterpreter
import OAI.MathematicalPhysics.NavierStokes.ForcedComputation.Programs.MachineDecisionInput
namespace OAI
/-! Discharge of the finite-table undecidability input, using the fixed
universal interpreter and Mathlib's proved halting theorem. -/
namespace ForcedComputation
theorem finiteMachineHaltingUndecidable : FiniteMachineHaltingUndecidable := by
rintro ⟨d, hd, hcorrect⟩
obtain ⟨M, input, hi, hM⟩ := FiniteMachine.exists_fixed_universal_machine
apply ComputablePred.halting_problem 0
apply ComputablePred.computable_iff.mpr
refine ⟨fun c : Nat.Partrec.Code => d (M, input (Encodable.encode c)),
hd.comp ((Computable.const M).pair (hi.comp Computable.encode)), ?_⟩
funext c
apply propext
have h := (hcorrect (M, input (Encodable.encode c)) (hM _).1).trans (hM _).2
simpa only [Denumerable.ofNat_encode] using h.symm
end ForcedComputation
end OAI
|