`BookProof.SmHiggsVacuum.gaugeMassForm_eq_zero_iff` (X : Fin 3 → Matrix (Fin 4) (Fin 4) ℝ) (u : Fin 4 → ℝ) : gaugeMassForm X u = 0 ↔ ∀ i, (X i).mulVec u = 0

Proved

BookProof.SmHiggsVacuum.gaugeMassForm_eq_zero_iff

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmHiggsVacuum.

BookProof.SmHiggsVacuum.gaugeMassForm_eq_zero_iff (X : Fin 3 → Matrix (Fin 4) (Fin 4) ℝ) (u : Fin 4 → ℝ) : gaugeMassForm X u = 0 ↔ ∀ i, (X i).mulVec u = 0

Formalization note: Lean 4 identifier BookProof.SmHiggsVacuum.gaugeMassForm_eq_zero_iff.

Preamble

-- Generated from ChapterSmHiggsVacuum.lean — theorem BookProof.SmHiggsVacuum.gaugeMassForm_eq_zero_iff
import Mathlib
import Definitions.Def_ChapterSmHiggsVacuum
open BookProof.SmHiggsVacuum



open Finset

noncomputable section

variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℝ E]

Formal statement

theorem BookProof.SmHiggsVacuum.gaugeMassForm_eq_zero_iff (X : Fin 3 → Matrix (Fin 4) (Fin 4) ℝ) (u : Fin 4 → ℝ) :
    gaugeMassForm X u = 0 ↔ ∀ i, (X i).mulVec u = 0 := by sorry

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