`BookProof.ChapterG3.qftVacuum_gauge_invariant` (k : ℕ) (L : EuclideanSpace ℝ (Fin k) ≃ₗᵢ[ℝ] EuclideanSpace ℝ (Fin k)) : (qftVacuum k).map L = qftVacuum k

Proved

BookProof.ChapterG3.qftVacuum_gauge_invariant

by leonardopedro · Oct 18, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterG3.

BookProof.ChapterG3.qftVacuum_gauge_invariant (k : ℕ) (L : EuclideanSpace ℝ (Fin k) ≃ₗᵢ[ℝ] EuclideanSpace ℝ (Fin k)) : (qftVacuum k).map L = qftVacuum k

Formalization note: Lean 4 identifier BookProof.ChapterG3.qftVacuum_gauge_invariant.

Preamble

-- Generated from ChapterG3.lean — theorem BookProof.ChapterG3.qftVacuum_gauge_invariant
import Mathlib
import Definitions.Def_ChapterG3
open BookProof.ChapterG3


open MeasureTheory
open scoped ENNReal



variable {X : Type*}

Formal statement

theorem BookProof.ChapterG3.qftVacuum_gauge_invariant (k : ℕ)
    (L : EuclideanSpace ℝ (Fin k) ≃ₗᵢ[ℝ] EuclideanSpace ℝ (Fin k)) :
    (qftVacuum k).map L = qftVacuum k := by sorry

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