Prove2Me

`BookProof.ChapterEulerGenericDensity.Jgen_mul` (l w : Fin d → ℝ) (hll : l ⬝ᵥ l = 1) (hww : w ⬝ᵥ w = 1) (hlw : l ⬝ᵥ w = 0) : (Matrix.vecMulVec l l - Matrix.vecMulVec w w) * Jgen l

Proved
BookProof.ChapterEulerGenericDensity.Jgen_mul

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEulerGenericDensity.

BookProof.ChapterEulerGenericDensity.Jgen_mul (l w : Fin d → ℝ) (hll : l ⬝ᵥ l = 1) (hww : w ⬝ᵥ w = 1) (hlw : l ⬝ᵥ w = 0) : (Matrix.vecMulVec l l - Matrix.vecMulVec w w) * Jgen l w = Matrix.vecMulVec l w + Matrix.vecMulVec w l

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

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


open scoped Matrix
open Matrix


variable {d : ℕ}
Formal statement
theorem BookProof.ChapterEulerGenericDensity.Jgen_mul (l w : Fin d → ℝ)
    (hll : l ⬝ᵥ l = 1) (hww : w ⬝ᵥ w = 1) (hlw : l ⬝ᵥ w = 0) :
    (Matrix.vecMulVec l l - Matrix.vecMulVec w w) * Jgen l w
      = Matrix.vecMulVec l w + Matrix.vecMulVec w l := by sorry

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