`BookProof.ChapterGravityPolymomentum.polyMom_contract_v_spatial` (hv : minkSq v = -1) (hS : IsSpatial v S) (hTc : IsSpatial v Tc) : (spatialProj v).mulVec ((polyMom e T S Tc u v).

Proved

BookProof.ChapterGravityPolymomentum.polyMom_contract_v_spatial

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGravityPolymomentum.

BookProof.ChapterGravityPolymomentum.polyMom_contract_v_spatial (hv : minkSq v = -1) (hS : IsSpatial v S) (hTc : IsSpatial v Tc) : (spatialProj v).mulVec ((polyMom e T S Tc u v).mulVec (lower v)) = (-2 * e) • (spatialProj v).mulVec u

Formalization note: Lean 4 identifier BookProof.ChapterGravityPolymomentum.polyMom_contract_v_spatial.

Preamble

-- Generated from ChapterGravityPolymomentum.lean — theorem BookProof.ChapterGravityPolymomentum.polyMom_contract_v_spatial
import Mathlib
import Definitions.Def_ChapterGravityPolymomentum
import Definitions.Def_ChapterGravityProjector
open BookProof.ChapterGravityProjector
open BookProof.ChapterGravityPolymomentum



open Matrix
open scoped BigOperators
open BookProof.ChapterGravityProjector

variable {e T : ℝ} {S Tc : Matrix (Fin 4) (Fin 4) ℝ} {u v : Fin 4 → ℝ}

Formal statement

theorem BookProof.ChapterGravityPolymomentum.polyMom_contract_v_spatial (hv : minkSq v = -1) (hS : IsSpatial v S)
    (hTc : IsSpatial v Tc) :
    (spatialProj v).mulVec ((polyMom e T S Tc u v).mulVec (lower v))
      = (-2 * e) • (spatialProj v).mulVec u := by sorry

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