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lemma proved tactic proof

sumFirst8_extendPeriodic_eq_Z

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formal statement (Lean)

  50lemma sumFirst8_extendPeriodic_eq_Z (w : Pattern 8) :
  51  sumFirst 8 (extendPeriodic8 w) = Z_of_window w := by

proof body

Tactic-mode proof.

  52  classical
  53  unfold sumFirst Z_of_window extendPeriodic8
  54  have hmod : ∀ i : Fin 8, (i.val % 8) = i.val := by
  55    intro i; exact Nat.mod_eq_of_lt i.isLt
  56  have hfun :
  57    (fun i : Fin 8 => (if w ⟨i.val % 8, Nat.mod_lt _ (by decide)⟩ then 1 else 0))
  58    = (fun i : Fin 8 => (if w i then 1 else 0)) := by
  59      funext i; simp [hmod i]
  60  have := congrArg (fun f => ∑ i : Fin 8, f i) hfun
  61  simpa using this
  62
  63end PatternLayer
  64
  65namespace MeasurementLayer
  66
  67open scoped BigOperators
  68open Finset PatternLayer
  69
  70/-- Sum of one 8‑tick sub‑block starting at index `j*8`. -/

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