`BookProof.ChapterGravityPolymomentum.trace_metric_mul_of_antisymm` {M : Matrix (Fin 4) (Fin 4) ℝ} (hM : Mᵀ = -M) : (metric * M).trace = 0

Proved

BookProof.ChapterGravityPolymomentum.trace_metric_mul_of_antisymm

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGravityPolymomentum.

BookProof.ChapterGravityPolymomentum.trace_metric_mul_of_antisymm {M : Matrix (Fin 4) (Fin 4) ℝ} (hM : Mᵀ = -M) : (metric * M).trace = 0

Formalization note: Lean 4 identifier BookProof.ChapterGravityPolymomentum.trace_metric_mul_of_antisymm.

Preamble

-- Generated from ChapterGravityPolymomentum.lean — theorem BookProof.ChapterGravityPolymomentum.trace_metric_mul_of_antisymm
import Mathlib
import Definitions.Def_ChapterGravityPolymomentum
import Definitions.Def_ChapterGravityProjector
open BookProof.ChapterGravityProjector
open BookProof.ChapterGravityPolymomentum



open Matrix
open scoped BigOperators
open BookProof.ChapterGravityProjector

Formal statement

theorem BookProof.ChapterGravityPolymomentum.trace_metric_mul_of_antisymm {M : Matrix (Fin 4) (Fin 4) ℝ} (hM : Mᵀ = -M) :
    (metric * M).trace = 0 := by sorry

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