Prove2Me

`BookProof.DirectSumEsa.fockH_essentiallySelfAdjointOn` {w : ℝ → ℝ} (hw : Measurable w) : EssentiallySelfAdjointOn (fockCore w) ((fockCore w).subtype.comp (fockH hw))

Proved
BookProof.DirectSumEsa.fockH_essentiallySelfAdjointOn

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterDirectSumEsa.

BookProof.DirectSumEsa.fockH_essentiallySelfAdjointOn {w : ℝ → ℝ} (hw : Measurable w) : EssentiallySelfAdjointOn (fockCore w) ((fockCore w).subtype.comp (fockH hw))

Formalization note: Lean 4 identifier BookProof.DirectSumEsa.fockH_essentiallySelfAdjointOn.

Preamble
-- Generated from ChapterDirectSumEsa.lean — theorem BookProof.DirectSumEsa.fockH_essentiallySelfAdjointOn
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterDirectSumEsa
import Definitions.Def_ChapterFarisLavineCore
open BookProof.DirectSumEsa


open scoped ENNReal


open BookProof.FarisLavine

noncomputable section

variable {ι : Type*} {G : ι → Type*} [∀ i, NormedAddCommGroup (G i)]
  [∀ i, InnerProductSpace ℂ (G i)]

variable {D : ∀ i, Submodule ℂ (G i)}
variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F]
Formal statement
theorem BookProof.DirectSumEsa.fockH_essentiallySelfAdjointOn {w : ℝ → ℝ} (hw : Measurable w) :
    EssentiallySelfAdjointOn (fockCore w) ((fockCore w).subtype.comp (fockH hw)) := by sorry

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