`BookProof.SmDiracYukawa.norm_dcommOp_le` {H N : FermiFock n →ₗ[ℂ] FermiFock n} {K Om : ℝ} (hK : ∀ ψ, ‖H ψ‖ ≤ K * ‖ψ‖) (hN : ∀ ψ, ‖N ψ‖ ≤ Om * ‖ψ‖) (hKn :...
ProvedBookProof.SmDiracYukawa.norm_dcommOp_letheoremstimepiece
Prove the following Lean 4 theorem from ChapterSmDiracYukawa.
BookProof.SmDiracYukawa.norm_dcommOp_le {H N : FermiFock n →ₗ[ℂ] FermiFock n} {K Om : ℝ} (hK : ∀ ψ, ‖H ψ‖ ≤ K * ‖ψ‖) (hN : ∀ ψ, ‖N ψ‖ ≤ Om * ‖ψ‖) (hKn : 0 ≤ K) (hOn : 0 ≤ Om) (ψ : FermiFock n) : ‖dcommOp H N ψ‖ ≤ 4 * K * Om ^ 2 * ‖ψ‖
Formalization note: Lean 4 identifier BookProof.SmDiracYukawa.norm_dcommOp_le.
Preamble
-- Generated from ChapterSmDiracYukawa.lean — theorem BookProof.SmDiracYukawa.norm_dcommOp_le
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterSmDiracYukawa
import Definitions.Def_ChapterSmCarAlgebra
open BookProof.SmCar
open BookProof.SmDiracYukawa
open Finset Matrix
open BookProof.SmCar BookProof.FarisLavine
variable {n : ℕ}
noncomputable section
variable {hD M : Matrix (Fin n) (Fin n) ℂ} {z : ℂ} {om : Fin n → ℝ} {c0 : ℝ}Formal statement
theorem BookProof.SmDiracYukawa.norm_dcommOp_le {H N : FermiFock n →ₗ[ℂ] FermiFock n} {K Om : ℝ}
(hK : ∀ ψ, ‖H ψ‖ ≤ K * ‖ψ‖) (hN : ∀ ψ, ‖N ψ‖ ≤ Om * ‖ψ‖) (hKn : 0 ≤ K) (hOn : 0 ≤ Om)
(ψ : FermiFock n) : ‖dcommOp H N ψ‖ ≤ 4 * K * Om ^ 2 * ‖ψ‖ := by sorry