protocolSpec_eq_iff

formal source

  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
  79  · intro h
  80    rw [h]
  81
  82/-- Distinct combinations have distinct complete empirical protocols. -/
  83theorem protocolSpec_ne_of_ne {a b : CombinationID} (h : a ≠ b) :
  84    protocolSpec a ≠ protocolSpec b := by
  85  intro hp
  86  exact h (protocolSpec_injective hp)
  87
  88theorem c1_c3_protocol_distinct :
  89    protocolSpec .c1CognitiveTensor ≠ protocolSpec .c3OncologyTensor := by
  90  exact protocolSpec_ne_of_ne (by decide)
  91
  92theorem c3_c5_protocol_distinct :
  93    protocolSpec .c3OncologyTensor ≠ protocolSpec .c5AttentionTensor := by
  94  exact protocolSpec_ne_of_ne (by decide)
  95
  96theorem c5_c8_protocol_distinct :
  97    protocolSpec .c5AttentionTensor ≠ protocolSpec .c8MillerSpan := by
  98  exact protocolSpec_ne_of_ne (by decide)
  99
 100/-- A theorem bundle is empirically covered if every combination has a falsifier
 101protocol. -/
 102def EmpiricallyCovered : Prop :=
 103  ∀ c : CombinationID, ProtocolFalsifiable c
 104