Prove2Me

`BookProof.ShiftedQuadraticMatrix.mulVec_matBoostVec` {A : Matrix (Fin d) (Fin d) ℝ} (hdet : IsUnit A.det) (b' : Fin d → ℝ) (i : Fin d) : ∑ j, A i j * (matBoostVec A b') j = -(b' i

Proved
BookProof.ShiftedQuadraticMatrix.mulVec_matBoostVec

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterShiftedQuadraticMatrixEsa.

BookProof.ShiftedQuadraticMatrix.mulVec_matBoostVec {A : Matrix (Fin d) (Fin d) ℝ} (hdet : IsUnit A.det) (b' : Fin d → ℝ) (i : Fin d) : ∑ j, A i j * (matBoostVec A b') j = -(b' i) / 2

Formalization note: Lean 4 identifier BookProof.ShiftedQuadraticMatrix.mulVec_matBoostVec.

Preamble
-- Generated from ChapterShiftedQuadraticMatrixEsa.lean — theorem BookProof.ShiftedQuadraticMatrix.mulVec_matBoostVec
import Definitions.Def_ChapterHermiteProductCore
import Definitions.Def_ChapterHermiteProductBasis
import Definitions.Def_ChapterNavierStokesDifferentialL2
import Definitions.Def_ChapterHyperbolicQuadraticEsa
import Definitions.Def_ChapterQuadraticRotationEsa
import Definitions.Def_ChapterShiftedHermiteCore
import Definitions.Def_ChapterShiftedQuadraticEsa
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterStoneBridge
import Definitions.Def_ChapterEsaClosureCore
import Definitions.Def_ChapterSirkTrotterKato
import Mathlib
import Definitions.Def_ChapterShiftedQuadraticMatrixEsa
open BookProof.ShiftedQuadraticMatrix



open MeasureTheory MvPolynomial Matrix
open BookProof.HermiteProductCore BookProof.HermiteProductBasis
open BookProof.NavierStokesFlow.DifferentialL2
open BookProof.HyperbolicQuadratic
open BookProof.QuadraticRotation
open BookProof.ShiftedHermiteCore
open BookProof.ShiftedQuadratic
open BookProof.FarisLavine
open BookProof.StoneBridge BookProof.EsaClosure BookProof.ChapterStoneResolvent

noncomputable section

variable {d : ℕ}
Formal statement
theorem BookProof.ShiftedQuadraticMatrix.mulVec_matBoostVec {A : Matrix (Fin d) (Fin d) ℝ} (hdet : IsUnit A.det)
    (b' : Fin d → ℝ) (i : Fin d) :
    ∑ j, A i j * (matBoostVec A b') j = -(b' i) / 2 := by sorry

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