(hi : ℕ → ℝ) {m n : ℕ} (hmn : m ≤ n) : runHi hi n ≤ runHi hi m

Proved

BookProof.RitzCertificate.runHi_antitone

by leonardopedro · Sep 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

timepiece

Lean 4 theorem BookProof.RitzCertificate.runHi_antitone (module BookProof.RitzCertificate), source chapter BookProof/ChapterRitzCertificate.lean.

Preamble

-- Generated from ChapterRitzCertificate.lean — theorem BookProof.RitzCertificate.runHi_antitone
import Mathlib
import Definitions.Def_ChapterRitzCertificate
open BookProof.RitzCertificate













noncomputable section

open Filter Topology


open BookProof.FockOneParticleGap BookProof.FockSecondQuantization
open BookProof.ChapterSirkRitzSpectrum BookProof.BandEnclosure


variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F] [CompleteSpace F]














variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F] [CompleteSpace F]

Formal statement

theorem BookProof.RitzCertificate.runHi_antitone (hi : ℕ → ℝ) {m n : ℕ} (hmn : m ≤ n) : runHi hi n ≤ runHi hi m := by sorry

Source

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

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