`BookProof.ChapterGravitySplit.split_unique` (v x s : Fin 4 → ℝ) (c : ℝ) (hv : minkSq v = -1) (hs : minkForm s v = 0) (hx : x = s + c • v) : s = spatialPart v x ∧ c • v = timePart

Proved

BookProof.ChapterGravitySplit.split_unique

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGravitySplit.

BookProof.ChapterGravitySplit.split_unique (v x s : Fin 4 → ℝ) (c : ℝ) (hv : minkSq v = -1) (hs : minkForm s v = 0) (hx : x = s + c • v) : s = spatialPart v x ∧ c • v = timePart v x

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

Preamble

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



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

Formal statement

theorem BookProof.ChapterGravitySplit.split_unique (v x s : Fin 4 → ℝ) (c : ℝ) (hv : minkSq v = -1)
    (hs : minkForm s v = 0) (hx : x = s + c • v) :
    s = spatialPart v x ∧ c • v = timePart v x := by sorry

View graph