`BookProof.ChapterGaugeAdjointAlgebra.weylEnergy_nonneg` {M : Type*} {κ : M → M → ℝ} (hpos : ∀ x : M, 0 ≤ κ x x) (π : Fin 3 → M) (B : Fin 3 → Fin 3 → M) : 0 ≤ weylEnergy κ π B

Proved

BookProof.ChapterGaugeAdjointAlgebra.weylEnergy_nonneg

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaugeAdjointAlgebra.

BookProof.ChapterGaugeAdjointAlgebra.weylEnergy_nonneg {M : Type*} {κ : M → M → ℝ} (hpos : ∀ x : M, 0 ≤ κ x x) (π : Fin 3 → M) (B : Fin 3 → Fin 3 → M) : 0 ≤ weylEnergy κ π B

Formalization note: Lean 4 identifier BookProof.ChapterGaugeAdjointAlgebra.weylEnergy_nonneg.

Preamble

-- Generated from ChapterGaugeAdjointAlgebra.lean — theorem BookProof.ChapterGaugeAdjointAlgebra.weylEnergy_nonneg
import Mathlib
import Definitions.Def_ChapterGaugeAdjointAlgebra
open BookProof.ChapterGaugeAdjointAlgebra




open Finset

variable {L : Type*} [LieRing L]

Formal statement

theorem BookProof.ChapterGaugeAdjointAlgebra.weylEnergy_nonneg {M : Type*} {κ : M → M → ℝ} (hpos : ∀ x : M, 0 ≤ κ x x)
    (π : Fin 3 → M) (B : Fin 3 → Fin 3 → M) :
    0 ≤ weylEnergy κ π B := by sorry

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