`BookProof.ChapterEulerGenericDensity.vecMulVec_mul_vecMulVec` (u v x y : Fin d → ℝ) : Matrix.vecMulVec u v * Matrix.vecMulVec x y = (v ⬝ᵥ x) • Matrix.vecMulVec u y

Proved

BookProof.ChapterEulerGenericDensity.vecMulVec_mul_vecMulVec

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEulerGenericDensity.

BookProof.ChapterEulerGenericDensity.vecMulVec_mul_vecMulVec (u v x y : Fin d → ℝ) : Matrix.vecMulVec u v * Matrix.vecMulVec x y = (v ⬝ᵥ x) • Matrix.vecMulVec u y

Formalization note: Lean 4 identifier BookProof.ChapterEulerGenericDensity.vecMulVec_mul_vecMulVec.

Preamble

-- Generated from ChapterEulerGenericDensity.lean — theorem BookProof.ChapterEulerGenericDensity.vecMulVec_mul_vecMulVec
import Mathlib
import Definitions.Def_ChapterEulerGenericDensity
open BookProof.ChapterEulerGenericDensity


open scoped Matrix
open Matrix


variable {d : ℕ}

Formal statement

theorem BookProof.ChapterEulerGenericDensity.vecMulVec_mul_vecMulVec (u v x y : Fin d → ℝ) :
    Matrix.vecMulVec u v * Matrix.vecMulVec x y = (v ⬝ᵥ x) • Matrix.vecMulVec u y := by sorry

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