`BookProof.DirectSumEsa.fockH_stone_flow` {w : ℝ → ℝ} (hw : Measurable w) : ∃ (T : ChapterStoneResolvent.UnboundedSelfAdjoint fockSpace) (U : ℝ → (fockSpace →L[ℂ] fockSpace)), EsaC

Proved

BookProof.DirectSumEsa.fockH_stone_flow

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterDirectSumEsa.

BookProof.DirectSumEsa.fockH_stone_flow {w : ℝ → ℝ} (hw : Measurable w) : ∃ (T : ChapterStoneResolvent.UnboundedSelfAdjoint fockSpace) (U : ℝ → (fockSpace →L[ℂ] fockSpace)), EsaClosure.IsSelfAdjointExtension ((fockCore w).subtype.comp (fockH hw)) T.op ∧ StoneBridge.IsStoneFlow T U

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

Preamble

-- Generated from ChapterDirectSumEsa.lean — theorem BookProof.DirectSumEsa.fockH_stone_flow
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterDirectSumEsa
import Definitions.Def_ChapterEsaClosureCore
import Definitions.Def_ChapterLinftyMultiplication
import Definitions.Def_ChapterNavierStokesFockContinuum
import Definitions.Def_ChapterStoneBridge
import Definitions.Def_ChapterStoneResolvent
open BookProof.EsaClosure
open BookProof.ChapterLinftyMultiplication
open BookProof.NavierStokesFlow.FockContinuum
open BookProof.StoneBridge
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_stone_flow {w : ℝ → ℝ} (hw : Measurable w) :
    ∃ (T : ChapterStoneResolvent.UnboundedSelfAdjoint fockSpace)
      (U : ℝ → (fockSpace →L[ℂ] fockSpace)),
      EsaClosure.IsSelfAdjointExtension ((fockCore w).subtype.comp (fockH hw)) T.op ∧
        StoneBridge.IsStoneFlow T U := by sorry

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