empty_balanced

formal source

  94  computeBalance page.events = 0
  95
  96/-- The empty page is balanced. -/
  97theorem empty_balanced : IsBalanced ⟨[], 0⟩ := by
  98  simp [IsBalanced, computeBalance]
  99
 100/-- **PROVED: Adding a paired event preserves balance.** -/
 101theorem paired_preserves_balance (page : LedgerPage)
 102    (h : IsBalanced page) (e : LedgerEvent) :
 103    IsBalanced ⟨page.events ++ [e, e.conj], 0⟩ := by
 104  rcases page with ⟨events, bal⟩
 105  simp [IsBalanced, computeBalance, List.foldl_append, LedgerEvent.conj] at h ⊢
 106  omega
 107
 108/-! ## §3. The Eight-Window Constraint -/
 109
 110/-- A **window** is a contiguous block of 8 events. -/
 111structure Window8 where
 112  /-- The 8 events in this window -/
 113  events : Fin 8 → LedgerEvent
 114
 115/-- The sum over a window. -/
 116def Window8.sum (w : Window8) : ℤ :=
 117  (Finset.univ.sum fun i => (w.events i).flow)
 118
 119/-- A window is **neutral** if its sum is zero. -/
 120def Window8.isNeutral (w : Window8) : Prop := w.sum = 0
 121
 122/-- **Construction: A neutral window from 4 paired events.** -/
 123def neutralWindow (e₁ e₂ e₃ e₄ : LedgerEvent) : Window8 where
 124  events := fun i =>
 125    match i with
 126    | ⟨0, _⟩ => e₁
 127    | ⟨1, _⟩ => e₁.conj