{T P : E →ₗ[ℂ] E} {thetaE thetaO deltaE deltaO : ℝ} (hEven : sectorGround T P 1 ≤ thetaE + deltaE) (hOdd : thetaO - deltaO ≤ sectorGround T P (-1)) (hsep : 0 < thetaO - thetaE - (deltaO +...

Proved

BookProof.SirkCertifiedGap.certified_parity_gap_pos

by leonardopedro · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

sirkspectral-theorytimepiece

Lean 4 theorem BookProof.SirkCertifiedGap.certified_parity_gap_pos (module BookProof.SirkCertifiedGap), source chapter BookProof/ChapterSirkCertifiedGap.lean.

Preamble

-- Generated from ChapterSirkCertifiedGap.lean — theorem BookProof.SirkCertifiedGap.certified_parity_gap_pos
import Mathlib
import Definitions.Def_ChapterSirkCertifiedGap
open BookProof.SirkCertifiedGap










noncomputable section


open scoped InnerProductSpace
open Finset Filter Topology
open BookProof.SirkFinitePrecision

variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℂ E] [FiniteDimensional ℂ E]

Formal statement

theorem BookProof.SirkCertifiedGap.certified_parity_gap_pos {T P : E →ₗ[ℂ] E} {thetaE thetaO deltaE deltaO : ℝ}
    (hEven : sectorGround T P 1 ≤ thetaE + deltaE)
    (hOdd : thetaO - deltaO ≤ sectorGround T P (-1))
    (hsep : 0 < thetaO - thetaE - (deltaO + deltaE)) :
    sectorGround T P 1 < sectorGround T P (-1) := by sorry

Source

https://github.com/leonardopedrio/timepiece/blob/61595bc/BookProof/ChapterSirkCertifiedGap.lean

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