`BookProof.ChapterGravityPolymomentum.contract_smul_left` (c : ℝ) (A B : Matrix (Fin 4) (Fin 4) ℝ) : contract (c • A) B = c * contract A B

Proved

BookProof.ChapterGravityPolymomentum.contract_smul_left

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGravityPolymomentum.

BookProof.ChapterGravityPolymomentum.contract_smul_left (c : ℝ) (A B : Matrix (Fin 4) (Fin 4) ℝ) : contract (c • A) B = c * contract A B

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

Preamble

-- Generated from ChapterGravityPolymomentum.lean — theorem BookProof.ChapterGravityPolymomentum.contract_smul_left
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.contract_smul_left (c : ℝ) (A B : Matrix (Fin 4) (Fin 4) ℝ) :
    contract (c • A) B = c * contract A B := by sorry

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