`BookProof.ChapterGravityPolymomentum.proj_polyMom` (hv : minkSq v = -1) (hS : IsSpatial v S) (hTc : IsSpatial v Tc) : proj v (polyMom e T S Tc u v) = e • (S - ((4 / 3) * T) • (met

Proved

BookProof.ChapterGravityPolymomentum.proj_polyMom

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGravityPolymomentum.

BookProof.ChapterGravityPolymomentum.proj_polyMom (hv : minkSq v = -1) (hS : IsSpatial v S) (hTc : IsSpatial v Tc) : proj v (polyMom e T S Tc u v) = e • (S - ((4 / 3) * T) • (metric + vecMulVec v v) - Tc)

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

Preamble

-- Generated from ChapterGravityPolymomentum.lean — theorem BookProof.ChapterGravityPolymomentum.proj_polyMom
import Mathlib
import Definitions.Def_ChapterGravityPolymomentum
import Definitions.Def_ChapterElectroweakFieldStrength
import Definitions.Def_ChapterGravityProjector
open BookProof.ChapterElectroweakFieldStrength
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.proj_polyMom (hv : minkSq v = -1) (hS : IsSpatial v S) (hTc : IsSpatial v Tc) :
    proj v (polyMom e T S Tc u v)
      = e • (S - ((4 / 3) * T) • (metric + vecMulVec v v) - Tc) := by sorry

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