`BookProof.QgCouplingDGammaSum.comparison_friedrichs` {s : Finset ι} {cols : ι → ℕ → (ℕ →₀ ℂ)} (hherm : ∀ i ∈ s, IsHermCol (cols i)) (hpos : ∀ i ∈ s, IsPosCol (cols i))...

Proved

BookProof.QgCouplingDGammaSum.comparison_friedrichs

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterQgCouplingDGammaSum.

BookProof.QgCouplingDGammaSum.comparison_friedrichs {s : Finset ι} {cols : ι → ℕ → (ℕ →₀ ℂ)} (hherm : ∀ i ∈ s, IsHermCol (cols i)) (hpos : ∀ i ∈ s, IsPosCol (cols i)) : ∃ (Dom : Submodule ℂ Fock) (A : Dom →ₗ[ℂ] Fock), IsPositiveSelfAdjointExtension (dGammaOp (comparisonCol s cols)) A

Formalization note: Lean 4 identifier BookProof.QgCouplingDGammaSum.comparison_friedrichs.

Preamble

-- Generated from ChapterQgCouplingDGammaSum.lean — theorem BookProof.QgCouplingDGammaSum.comparison_friedrichs
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Definitions.Def_ChapterNavierStokesIkebeKato
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterFriedrichsExtension
import Mathlib
import Definitions.Def_ChapterQgCouplingDGammaSum
import Definitions.Def_ChapterFockOneParticleGap
import Definitions.Def_ChapterFockSecondQuantization
import Definitions.Def_ChapterNavierStokesEsa
import Definitions.Def_ChapterYangMillsFriedrichs
open BookProof.FockOneParticleGap
open BookProof.FockSecondQuantization
open BookProof.YangMillsFriedrichs
open BookProof.QgCouplingDGammaSum



open BookProof.FockSecondQuantization
open BookProof.NavierStokesFlow BookProof.NavierStokesFlow.IkebeKato
open BookProof.FarisLavine BookProof.FriedrichsExtension BookProof.YangMillsFriedrichs

noncomputable section

variable {ι : Type*}

Formal statement

theorem BookProof.QgCouplingDGammaSum.comparison_friedrichs {s : Finset ι} {cols : ι → ℕ → (ℕ →₀ ℂ)}
    (hherm : ∀ i ∈ s, IsHermCol (cols i)) (hpos : ∀ i ∈ s, IsPosCol (cols i)) :
    ∃ (Dom : Submodule ℂ Fock) (A : Dom →ₗ[ℂ] Fock),
      IsPositiveSelfAdjointExtension (dGammaOp (comparisonCol s cols)) A := by sorry

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