`BookProof.ChapterGravityPolymomentum.trace_vecMulVec` (w u : Fin 4 → ℝ) : (vecMulVec w u).trace = ∑ a, w a * u a

Proved

BookProof.ChapterGravityPolymomentum.trace_vecMulVec

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGravityPolymomentum.

BookProof.ChapterGravityPolymomentum.trace_vecMulVec (w u : Fin 4 → ℝ) : (vecMulVec w u).trace = ∑ a, w a * u a

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

Preamble

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



open Matrix
open scoped BigOperators
open BookProof.ChapterGravityProjector

Formal statement

theorem BookProof.ChapterGravityPolymomentum.trace_vecMulVec (w u : Fin 4 → ℝ) :
    (vecMulVec w u).trace = ∑ a, w a * u a := by sorry

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