`BookProof.OperatorSeries.commForm_eq_neg_two_im` (H N : D →ₗ[ℂ] F) (x : D) : commForm H N x = -2 * (inner ℂ (H x) (N x) : ℂ).im

Proved

BookProof.OperatorSeries.commForm_eq_neg_two_im

by leonardopedro · Oct 5, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterOperatorSeriesEsa.

BookProof.OperatorSeries.commForm_eq_neg_two_im (H N : D →ₗ[ℂ] F) (x : D) : commForm H N x = -2 * (inner ℂ (H x) (N x) : ℂ).im

Formalization note: Lean 4 identifier BookProof.OperatorSeries.commForm_eq_neg_two_im.

Preamble

-- Generated from ChapterOperatorSeriesEsa.lean — theorem BookProof.OperatorSeries.commForm_eq_neg_two_im
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Definitions.Def_ChapterNavierStokesIkebeKato
import Definitions.Def_ChapterNavierStokesDeficiency
import Mathlib
import Definitions.Def_ChapterOperatorSeriesEsa
import Definitions.Def_ChapterFarisLavineCore
open BookProof.OperatorSeries

variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F] {D : Submodule ℂ F}



open BookProof.FarisLavine BookProof.NavierStokesFlow BookProof.NavierStokesFlow.IkebeKato
open BookProof.NavierStokesFlow.LpNat

noncomputable section

Formal statement

theorem BookProof.OperatorSeries.commForm_eq_neg_two_im (H N : D →ₗ[ℂ] F) (x : D) :
    commForm H N x = -2 * (inner ℂ (H x) (N x) : ℂ).im := by sorry

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