`BookProof.ChapterGravityPolymomentum.mul_spatialProj_transpose` (v : Fin 4 → ℝ) (M : Matrix (Fin 4) (Fin 4) ℝ) : M * (spatialProj v)ᵀ = M + vecMulVec (M.mulVec (lower v)) v

Proved

BookProof.ChapterGravityPolymomentum.mul_spatialProj_transpose

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGravityPolymomentum.

BookProof.ChapterGravityPolymomentum.mul_spatialProj_transpose (v : Fin 4 → ℝ) (M : Matrix (Fin 4) (Fin 4) ℝ) : M * (spatialProj v)ᵀ = M + vecMulVec (M.mulVec (lower v)) v

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

Preamble

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



open Matrix
open scoped BigOperators
open BookProof.ChapterGravityProjector

Formal statement

theorem BookProof.ChapterGravityPolymomentum.mul_spatialProj_transpose (v : Fin 4 → ℝ) (M : Matrix (Fin 4) (Fin 4) ℝ) :
    M * (spatialProj v)ᵀ = M + vecMulVec (M.mulVec (lower v)) v := by sorry

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