`BookProof.ChapterF7.anticomm_l2Symmetric` {K V : 𝓢(ℝ, ℂ) →L[ℂ] 𝓢(ℝ, ℂ)} (hK : IsL2Symmetric K) (hV : IsL2Symmetric V) : IsL2Symmetric (K.comp V + V.comp K)

Proved

BookProof.ChapterF7.anticomm_l2Symmetric

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterF7.

BookProof.ChapterF7.anticomm_l2Symmetric {K V : 𝓢(ℝ, ℂ) →L[ℂ] 𝓢(ℝ, ℂ)} (hK : IsL2Symmetric K) (hV : IsL2Symmetric V) : IsL2Symmetric (K.comp V + V.comp K)

Formalization note: Lean 4 identifier BookProof.ChapterF7.anticomm_l2Symmetric.

Preamble

-- Generated from ChapterF7.lean — theorem BookProof.ChapterF7.anticomm_l2Symmetric
import Mathlib
import Definitions.Def_ChapterF7
open BookProof.ChapterF7


open SchwartzMap MeasureTheory Complex
open scoped BigOperators


noncomputable section

Formal statement

theorem BookProof.ChapterF7.anticomm_l2Symmetric {K V : 𝓢(ℝ, ℂ) →L[ℂ] 𝓢(ℝ, ℂ)}
    (hK : IsL2Symmetric K) (hV : IsL2Symmetric V) :
    IsL2Symmetric (K.comp V + V.comp K) := by sorry

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