`BookProof.ScalarDGamma.norm_fockSectorOp_scalar_le` (n : ℕ) (x : fockSectorDom Hs ⊤ n) : ‖fockSectorOp Hs ⊤ (scalarOp Hs c) n x‖ ≤ ((n : ℝ) * |c|) * ‖(x : fockSector Hs n)‖

Proved

BookProof.ScalarDGamma.norm_fockSectorOp_scalar_le

by leonardopedro · Oct 25, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterScalarDGammaEsa.

BookProof.ScalarDGamma.norm_fockSectorOp_scalar_le (n : ℕ) (x : fockSectorDom Hs ⊤ n) : ‖fockSectorOp Hs ⊤ (scalarOp Hs c) n x‖ ≤ ((n : ℝ) * |c|) * ‖(x : fockSector Hs n)‖

Formalization note: Lean 4 identifier BookProof.ScalarDGamma.norm_fockSectorOp_scalar_le.

Preamble

-- Generated from ChapterScalarDGammaEsa.lean — theorem BookProof.ScalarDGamma.norm_fockSectorOp_scalar_le
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterGraphCoreTransfer
import Mathlib
import Definitions.Def_ChapterScalarDGammaEsa
import Definitions.Def_ChapterTensorGraphCore
import Definitions.Def_ChapterSecondQuantizationCoreEsa
import Definitions.Def_ChapterPermutationSectorEsa
import Definitions.Def_ChapterScalarDGammaEsa
open BookProof.TensorCore
open BookProof.ScalarDGamma



open scoped TensorProduct
open BookProof.FarisLavine BookProof.GraphCore BookProof.TensorCore
open BookProof.SecondQuantizationCore

noncomputable section

variable (Hs : IPSpace) (c : ℝ)

Formal statement

theorem BookProof.ScalarDGamma.norm_fockSectorOp_scalar_le (n : ℕ) (x : fockSectorDom Hs ⊤ n) :
    ‖fockSectorOp Hs ⊤ (scalarOp Hs c) n x‖ ≤ ((n : ℝ) * |c|) * ‖(x : fockSector Hs n)‖ := by sorry

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