natDegree_preΨ — Mathlib

English

For W and integer n, (W.preΨ' n).natDegree ≤ (n^2 - if Even n then 4 else 1)/2.

Русский

Для W и целого n: (W.preΨ' n).natDegree ≤ (n^2 - if Even n then 4 else 1)/2.

LaTeX

$$(W.preΨ' n).natDegree ≤ \frac{n^2 - (\text{if Even}(n) \text{ then } 4 \text{ else } 1)}{2}$$

Lean4

@[simp]
theorem natDegree_preΨ {n : ℤ} (h : (n : R) ≠ 0) :
    (W.preΨ n).natDegree = (n.natAbs ^ 2 - if Even n then 4 else 1) / 2 :=
  natDegree_eq_of_le_of_coeff_ne_zero (W.natDegree_preΨ_le n) <| W.coeff_preΨ_ne_zero h

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