`BookProof.ChapterGravityProjDirectSum.range_spatial_eq_ker_time` (v : Fin 4 → ℝ) (hv : minkSq v = -1) : LinearMap.range (spatialProj v).mulVecLin = LinearMap.ker (timeProj v).mulV

Proved

BookProof.ChapterGravityProjDirectSum.range_spatial_eq_ker_time

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGravityProjDirectSum.

BookProof.ChapterGravityProjDirectSum.range_spatial_eq_ker_time (v : Fin 4 → ℝ) (hv : minkSq v = -1) : LinearMap.range (spatialProj v).mulVecLin = LinearMap.ker (timeProj v).mulVecLin

Formalization note: Lean 4 identifier BookProof.ChapterGravityProjDirectSum.range_spatial_eq_ker_time.

Preamble

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


open Matrix


open BookProof.ChapterGravityProjector
open BookProof.ChapterGravityTimeProj

Formal statement

theorem BookProof.ChapterGravityProjDirectSum.range_spatial_eq_ker_time (v : Fin 4 → ℝ) (hv : minkSq v = -1) :
    LinearMap.range (spatialProj v).mulVecLin
      = LinearMap.ker (timeProj v).mulVecLin := by sorry

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