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

Proved

BookProof.SirkGapTable.certified_gap_mem_interval

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

sirkspectral-theorytimepiece

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

Preamble

-- Generated from ChapterSirkGapTable.lean — theorem BookProof.SirkGapTable.certified_gap_mem_interval
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.certified_gap_mem_interval {T P : E →ₗ[ℂ] E} {thetaE thetaO deltaE deltaO : ℝ}
    (hEvenHi : sectorGround T P 1 ≤ thetaE + deltaE)
    (hEvenLo : thetaE - deltaE ≤ sectorGround T P 1)
    (hOddLo : thetaO - deltaO ≤ sectorGround T P (-1))
    (hOddHi : sectorGround T P (-1) ≤ thetaO + deltaO) :
    sectorGround T P (-1) - sectorGround T P 1 ∈
      Set.Icc (thetaO - thetaE - (deltaO + deltaE)) (thetaO - thetaE + (deltaO + deltaE)) := by sorry

Source

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

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