`BookProof.QgCouplingDGammaSum.dGammaOp_diagCol_eq` (lam : ℕ → ℝ) : dGammaOp (diagCol lam) = (diagMax (occEnergy lam)).comp (Submodule.inclusion (finiteModes_le_maxDom (occEnergy l

Proved

BookProof.QgCouplingDGammaSum.dGammaOp_diagCol_eq

by leonardopedro · Oct 11, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterQgCouplingDGammaSum.

BookProof.QgCouplingDGammaSum.dGammaOp_diagCol_eq (lam : ℕ → ℝ) : dGammaOp (diagCol lam) = (diagMax (occEnergy lam)).comp (Submodule.inclusion (finiteModes_le_maxDom (occEnergy lam)))

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

Preamble

-- Generated from ChapterQgCouplingDGammaSum.lean — theorem BookProof.QgCouplingDGammaSum.dGammaOp_diagCol_eq
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterFriedrichsExtension
import Definitions.Def_ChapterYangMillsFriedrichs
import Mathlib
import Definitions.Def_ChapterQgCouplingDGammaSum
import Definitions.Def_ChapterFockOneParticleGap
import Definitions.Def_ChapterFockSecondQuantization
import Definitions.Def_ChapterNavierStokesEsa
import Definitions.Def_ChapterNavierStokesIkebeKato
open BookProof.FockOneParticleGap
open BookProof.FockSecondQuantization
open BookProof.NavierStokesFlow.IkebeKato
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.dGammaOp_diagCol_eq (lam : ℕ → ℝ) :
    dGammaOp (diagCol lam)
      = (diagMax (occEnergy lam)).comp
          (Submodule.inclusion (finiteModes_le_maxDom (occEnergy lam))) := by sorry

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