{ι : Type*} {l : Filter ι} (Tn : ι → F →L[ℂ] F) (T : F →L[ℂ] F) (k : ℕ) (hne : (minmaxSet T k).Nonempty) (h : Tendsto (fun i => ‖Tn i - T‖) l (𝓝 0)) : Tendsto (fun i => minmaxLevel (Tn i) k) l (𝓝...

Proved

BookProof.RitzPerturbation.minmaxLevel_tendsto_of_tendsto

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

timepiece

Lean 4 theorem BookProof.RitzPerturbation.minmaxLevel_tendsto_of_tendsto (module BookProof.RitzPerturbation), source chapter BookProof/ChapterRitzPerturbation.lean.

Preamble

-- Generated from ChapterSirkRitzPerturbation.lean — theorem BookProof.RitzPerturbation.minmaxLevel_tendsto_of_tendsto
import Mathlib
import Definitions.Def_ChapterSirkRitzPerturbation
open BookProof.RitzPerturbation








noncomputable section


open BookProof.RitzMinMax BookProof.ChapterSirkRitzSpectrum BookProof.HermiteGalerkin
open Filter Topology

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

Formal statement

theorem BookProof.RitzPerturbation.minmaxLevel_tendsto_of_tendsto {ι : Type*} {l : Filter ι} (Tn : ι → F →L[ℂ] F)
    (T : F →L[ℂ] F) (k : ℕ) (hne : (minmaxSet T k).Nonempty)
    (h : Tendsto (fun i => ‖Tn i - T‖) l (𝓝 0)) :
    Tendsto (fun i => minmaxLevel (Tn i) k) l (𝓝 (minmaxLevel T k)) := by sorry

Source

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

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