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

Proved

BookProof.SirkGapTable.gap_le_of_certificate

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

sirkspectral-theorytimepiece

Lean 4 theorem BookProof.SirkGapTable.gap_le_of_certificate (module BookProof.SirkGapTable), source chapter BookProof/ChapterSirkGapTable.lean.

Preamble

-- Generated from ChapterSirkGapTable.lean — theorem BookProof.SirkGapTable.gap_le_of_certificate
import Mathlib
import Definitions.Def_ChapterSirkGapTable
open BookProof.SirkGapTable









noncomputable section


open BookProof.SirkCertifiedGap



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

Formal statement

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

Source

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

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