`BookProof.ChapterGravitySplit.parts_orthogonal` (v x : Fin 4 → ℝ) (hv : minkSq v = -1) : minkForm (spatialPart v x) (timePart v x) = 0

Proved

BookProof.ChapterGravitySplit.parts_orthogonal

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGravitySplit.

BookProof.ChapterGravitySplit.parts_orthogonal (v x : Fin 4 → ℝ) (hv : minkSq v = -1) : minkForm (spatialPart v x) (timePart v x) = 0

Formalization note: Lean 4 identifier BookProof.ChapterGravitySplit.parts_orthogonal.

Preamble

-- Generated from ChapterGravitySplit.lean — theorem BookProof.ChapterGravitySplit.parts_orthogonal
import Definitions.Def_ChapterGravityTimeProj
import Mathlib
import Definitions.Def_ChapterGravitySplit
import Definitions.Def_ChapterGravityProjector
open BookProof.ChapterGravityProjector
open BookProof.ChapterGravitySplit



open Matrix
open scoped BigOperators
open BookProof.ChapterGravityProjector
open BookProof.ChapterGravityTimeProj

Formal statement

theorem BookProof.ChapterGravitySplit.parts_orthogonal (v x : Fin 4 → ℝ) (hv : minkSq v = -1) :
    minkForm (spatialPart v x) (timePart v x) = 0 := by sorry

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