`BookProof.ChapterGravityTimeProj.timeProj_mul_spatialProj` (v : Fin 4 → ℝ) (hv : minkSq v = -1) : timeProj v * spatialProj v = 0

Proved

BookProof.ChapterGravityTimeProj.timeProj_mul_spatialProj

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGravityTimeProj.

BookProof.ChapterGravityTimeProj.timeProj_mul_spatialProj (v : Fin 4 → ℝ) (hv : minkSq v = -1) : timeProj v * spatialProj v = 0

Formalization note: Lean 4 identifier BookProof.ChapterGravityTimeProj.timeProj_mul_spatialProj.

Preamble

-- Generated from ChapterGravityTimeProj.lean — theorem BookProof.ChapterGravityTimeProj.timeProj_mul_spatialProj
import Mathlib
import Definitions.Def_ChapterGravityTimeProj
import Definitions.Def_ChapterGravityProjector
open BookProof.ChapterGravityProjector
open BookProof.ChapterGravityTimeProj



open Matrix
open scoped BigOperators
open BookProof.ChapterGravityProjector

Formal statement

theorem BookProof.ChapterGravityTimeProj.timeProj_mul_spatialProj (v : Fin 4 → ℝ) (hv : minkSq v = -1) :
    timeProj v * spatialProj v = 0 := by sorry

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