eventCompose

formal source

  31  · have h' : b ≠ a := by intro hb; exact h hb.symm
  32    simp [eventCost, h, h']
  33
  34def eventCompose (a b : EventState) : EventState :=
  35  { act := a.act + b.act, beat := a.beat + b.beat }
  36
  37def narrativeZero : EventState := ⟨0, 0⟩
  38def incitingBeat : EventState := ⟨0, 1⟩
  39
  40/-- Strict narrative realization using beat succession as the generator. -/
  41def strictNarrativeRealization : StrictLogicRealization where
  42  Carrier := EventState
  43  Cost := Nat
  44  zeroCost := inferInstance
  45  compare := eventCost
  46  compose := eventCompose
  47  one := narrativeZero
  48  generator := incitingBeat
  49  identity_law := eventCost_self
  50  non_contradiction_law := eventCost_symm
  51  excluded_middle_law := True
  52  composition_law := True
  53  invariance_law := True
  54  nontrivial_law := by
  55    simp [eventCost, incitingBeat, narrativeZero]
  56
  57def narrative_arith_equiv_logicNat :
  58    (StrictLogicRealization.arith strictNarrativeRealization).peano.carrier
  59      ≃ ArithmeticFromLogic.LogicNat :=
  60  (StrictLogicRealization.toLightweight strictNarrativeRealization).orbitEquivLogicNat
  61
  62end Narrative
  63end Strict
  64end UniversalForcing