`BookProof.QgCouplingDGammaSum.creA_annA_apply` (k : ℕ) (u : FockAlg) (α : Conf) : creA k (annA k u) α = ((α k : ℝ) : ℂ) * u α

Proved

BookProof.QgCouplingDGammaSum.creA_annA_apply

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterQgCouplingDGammaSum.

BookProof.QgCouplingDGammaSum.creA_annA_apply (k : ℕ) (u : FockAlg) (α : Conf) : creA k (annA k u) α = ((α k : ℝ) : ℂ) * u α

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

Preamble

-- Generated from ChapterQgCouplingDGammaSum.lean — theorem BookProof.QgCouplingDGammaSum.creA_annA_apply
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Definitions.Def_ChapterNavierStokesIkebeKato
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterFriedrichsExtension
import Definitions.Def_ChapterYangMillsFriedrichs
import Mathlib
import Definitions.Def_ChapterQgCouplingDGammaSum
import Definitions.Def_ChapterFockSecondQuantization
import Definitions.Def_ChapterNavierStokesFockCanonical
open BookProof.FockSecondQuantization
open BookProof.NavierStokesFlow.FockCanonical
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.creA_annA_apply (k : ℕ) (u : FockAlg) (α : Conf) :
    creA k (annA k u) α = ((α k : ℝ) : ℂ) * u α := by sorry

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