Prove2Me

`BookProof.ShiftedQuadratic.shiftedHOp_symmetric` (c b b' : Fin d → ℝ) (hc : ∀ i, c i ≠ 0) : SymmetricOn (polyGaussCoreT (shiftVec c b) (boostVec c b')) (shiftedHOp (shiftVec c b)

Proved
BookProof.ShiftedQuadratic.shiftedHOp_symmetric

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterShiftedQuadraticEsa.

BookProof.ShiftedQuadratic.shiftedHOp_symmetric (c b b' : Fin d → ℝ) (hc : ∀ i, c i ≠ 0) : SymmetricOn (polyGaussCoreT (shiftVec c b) (boostVec c b')) (shiftedHOp (shiftVec c b) (boostVec c b') c b b')

Formalization note: Lean 4 identifier BookProof.ShiftedQuadratic.shiftedHOp_symmetric.

Preamble
-- Generated from ChapterShiftedQuadraticEsa.lean — theorem BookProof.ShiftedQuadratic.shiftedHOp_symmetric
import Definitions.Def_ChapterHermiteProductBasis
import Definitions.Def_ChapterNavierStokesDifferentialL2
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterStoneBridge
import Definitions.Def_ChapterEsaClosureCore
import Definitions.Def_ChapterSirkTrotterKato
import Mathlib
import Definitions.Def_ChapterShiftedQuadraticEsa
import Definitions.Def_ChapterFarisLavineCore
import Definitions.Def_ChapterHermiteProductCore
import Definitions.Def_ChapterHyperbolicQuadraticEsa
import Definitions.Def_ChapterShiftedHermiteCore
open BookProof.HermiteProductCore
open BookProof.HyperbolicQuadratic
open BookProof.ShiftedHermiteCore
open BookProof.ShiftedQuadratic



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

noncomputable section

variable {d : ℕ}
Formal statement
theorem BookProof.ShiftedQuadratic.shiftedHOp_symmetric (c b b' : Fin d → ℝ) (hc : ∀ i, c i ≠ 0) :
    SymmetricOn (polyGaussCoreT (shiftVec c b) (boostVec c b'))
      (shiftedHOp (shiftVec c b) (boostVec c b') c b b') := by sorry

View graph