Window8

formal source

 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
 128    | ⟨2, _⟩ => e₂
 129    | ⟨3, _⟩ => e₂.conj
 130    | ⟨4, _⟩ => e₃
 131    | ⟨5, _⟩ => e₃.conj
 132    | ⟨6, _⟩ => e₄
 133    | ⟨7, _⟩ => e₄.conj
 134
 135/-- **PROVED: A window of paired events is neutral.** -/
 136theorem neutralWindow_isNeutral (e₁ e₂ e₃ e₄ : LedgerEvent) :
 137    (neutralWindow e₁ e₂ e₃ e₄).isNeutral := by
 138  simp [Window8.isNeutral, Window8.sum, neutralWindow, LedgerEvent.conj, Fin.sum_univ_eight]
 139
 140/-! ## §4. The Graded Ledger -/
 141