`BookProof.ChapterGaugeCasimirAverage.casimir_apply_eq_zero_iff` (T : ι → V →ₗ[ℂ] V) (hT : ∀ a, (T a).IsSymmetric) (v : V) : casimir T v = 0 ↔ ∀ a, T a v = 0

Proved

BookProof.ChapterGaugeCasimirAverage.casimir_apply_eq_zero_iff

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaugeCasimirAverage.

BookProof.ChapterGaugeCasimirAverage.casimir_apply_eq_zero_iff (T : ι → V →ₗ[ℂ] V) (hT : ∀ a, (T a).IsSymmetric) (v : V) : casimir T v = 0 ↔ ∀ a, T a v = 0

Formalization note: Lean 4 identifier BookProof.ChapterGaugeCasimirAverage.casimir_apply_eq_zero_iff.

Preamble

-- Generated from ChapterGaugeCasimirAverage.lean — theorem BookProof.ChapterGaugeCasimirAverage.casimir_apply_eq_zero_iff
import Definitions.Def_ChapterGaugeIncompleteFixing
import Mathlib
import Definitions.Def_ChapterGaugeCasimirAverage
open BookProof.ChapterGaugeCasimirAverage



open BookProof.ChapterGaugeIncompleteFixing
open MeasureTheory
open scoped InnerProductSpace

variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℂ V]
variable {ι : Type*} [Fintype ι]

Formal statement

theorem BookProof.ChapterGaugeCasimirAverage.casimir_apply_eq_zero_iff (T : ι → V →ₗ[ℂ] V) (hT : ∀ a, (T a).IsSymmetric)
    (v : V) : casimir T v = 0 ↔ ∀ a, T a v = 0 := by sorry

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