Prove2Me

`BookProof.ShiftedQuadratic.shiftedHOp_not_bounded` (c b b' : Fin d → ℝ) (hc : ∀ i, c i ≠ 0) {i : Fin d} : ¬ ∃ C : ℝ, ∀ f : polyGaussCoreT (shiftVec c b) (boostVec c b'), ‖shiftedH

Proved
BookProof.ShiftedQuadratic.shiftedHOp_not_bounded

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterShiftedQuadraticEsa.

BookProof.ShiftedQuadratic.shiftedHOp_not_bounded (c b b' : Fin d → ℝ) (hc : ∀ i, c i ≠ 0) {i : Fin d} : ¬ ∃ C : ℝ, ∀ f : polyGaussCoreT (shiftVec c b) (boostVec c b'), ‖shiftedHOp (shiftVec c b) (boostVec c b') c b b' f‖ ≤ C * ‖(f : L2d d)‖

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

Preamble
-- Generated from ChapterShiftedQuadraticEsa.lean — theorem BookProof.ShiftedQuadratic.shiftedHOp_not_bounded
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_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_not_bounded (c b b' : Fin d → ℝ) (hc : ∀ i, c i ≠ 0) {i : Fin d} :
    ¬ ∃ C : ℝ, ∀ f : polyGaussCoreT (shiftVec c b) (boostVec c b'),
        ‖shiftedHOp (shiftVec c b) (boostVec c b') c b b' f‖ ≤ C * ‖(f : L2d d)‖ := by sorry

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