Prove2Me

`BookProof.ChapterGravityProjDirectSum.isCompl_spatial_time_range` (v : Fin 4 → ℝ) (hv : minkSq v = -1) : IsCompl (LinearMap.range (spatialProj v).mulVecLin) (LinearMap.range (time

Proved
BookProof.ChapterGravityProjDirectSum.isCompl_spatial_time_range

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGravityProjDirectSum.

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

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

Preamble
-- Generated from ChapterGravityProjDirectSum.lean — theorem BookProof.ChapterGravityProjDirectSum.isCompl_spatial_time_range
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.isCompl_spatial_time_range (v : Fin 4 → ℝ) (hv : minkSq v = -1) :
    IsCompl (LinearMap.range (spatialProj v).mulVecLin)
      (LinearMap.range (timeProj v).mulVecLin) := by sorry

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