`BookProof.ChapterGravityPolymomentum.trace_metric_mul_spatialMetric` (v : Fin 4 → ℝ) (hv : minkSq v = -1) : (metric * (metric + vecMulVec v v)).trace = 3

Proved

BookProof.ChapterGravityPolymomentum.trace_metric_mul_spatialMetric

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_spatialMetric (v : Fin 4 → ℝ) (hv : minkSq v = -1) : (metric * (metric + vecMulVec v v)).trace = 3

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

Preamble

-- Generated from ChapterGravityPolymomentum.lean — theorem BookProof.ChapterGravityPolymomentum.trace_metric_mul_spatialMetric
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_spatialMetric (v : Fin 4 → ℝ) (hv : minkSq v = -1) :
    (metric * (metric + vecMulVec v v)).trace = 3 := by sorry

View graph