Prove2Me

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

Proved
BookProof.ChapterEulerGenericDensity.Jgen_sq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEulerGenericDensity.

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

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

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


open scoped Matrix
open Matrix


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

View graph