ProtocolMatches

formal source

  45  exact ⟨datasetClass c, predictedObservable c, failureMode c, rfl, rfl, rfl⟩
  46
  47/-- A concrete protocol record matches a combination when all three fields agree. -/
  48def ProtocolMatches (c : CombinationID) (p : ProtocolSpec) : Prop :=
  49  p.dataset = datasetClass c ∧
  50    p.observable = predictedObservable c ∧
  51    p.failure = failureMode c
  52
  53theorem protocolSpec_matches (c : CombinationID) :
  54    ProtocolMatches c (protocolSpec c) := by
  55  simp [ProtocolMatches, protocolSpec]
  56
  57/-- Each implemented combination has a unique empirical protocol record. -/
  58theorem uniqueProtocolSpec (c : CombinationID) :
  59    ∃! p : ProtocolSpec, ProtocolMatches c p := by
  60  refine ⟨protocolSpec c, protocolSpec_matches c, ?_⟩
  61  intro p hp
  62  rcases p with ⟨d, o, f⟩
  63  rcases hp with ⟨hd, ho, hf⟩
  64  simp [protocolSpec] at hd ho hf ⊢
  65  exact ⟨hd, ho, hf⟩
  66
  67/-- Distinct combinations have distinct protocol records. -/
  68theorem protocolSpec_injective : Function.Injective protocolSpec := by
  69  intro a b h
  70  apply datasetClass_injective
  71  exact congrArg ProtocolSpec.dataset h
  72
  73/-- Equality of empirical protocols is exactly equality of combinations. -/
  74theorem protocolSpec_eq_iff (a b : CombinationID) :
  75    protocolSpec a = protocolSpec b ↔ a = b := by
  76  constructor
  77  · intro h
  78    exact protocolSpec_injective h