`BookProof.ChapterGravityInvMetric.invSpatialMetric_mul_spatialMetric` (v : Fin 4 → ℝ) (hv : minkSq v = -1) : invSpatialMetric v * spatialMetric v = spatialProj v

Proved

BookProof.ChapterGravityInvMetric.invSpatialMetric_mul_spatialMetric

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGravityInvMetric.

BookProof.ChapterGravityInvMetric.invSpatialMetric_mul_spatialMetric (v : Fin 4 → ℝ) (hv : minkSq v = -1) : invSpatialMetric v * spatialMetric v = spatialProj v

Formalization note: Lean 4 identifier BookProof.ChapterGravityInvMetric.invSpatialMetric_mul_spatialMetric.

Preamble

-- Generated from ChapterGravityInvMetric.lean — theorem BookProof.ChapterGravityInvMetric.invSpatialMetric_mul_spatialMetric
import Mathlib
import Definitions.Def_ChapterGravityInvMetric
import Definitions.Def_ChapterGravityMetric
import Definitions.Def_ChapterGravityProjector
open BookProof.ChapterGravityMetric
open BookProof.ChapterGravityProjector
open BookProof.ChapterGravityInvMetric



open Matrix
open scoped BigOperators
open BookProof.ChapterGravityProjector
open BookProof.ChapterGravityMetric

Formal statement

theorem BookProof.ChapterGravityInvMetric.invSpatialMetric_mul_spatialMetric (v : Fin 4 → ℝ) (hv : minkSq v = -1) :
    invSpatialMetric v * spatialMetric v = spatialProj v := by sorry

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