`BookProof.QgCouplingDGammaSum.dGammaOp_finsetSum_col` (s : Finset ι) (cols : ι → ℕ → (ℕ →₀ ℂ)) (x : lpFiniteModes Conf) : dGammaOp (fun k => ∑ i ∈ s, cols i k) x = ∑ i ∈...

Proved

BookProof.QgCouplingDGammaSum.dGammaOp_finsetSum_col

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterQgCouplingDGammaSum.

BookProof.QgCouplingDGammaSum.dGammaOp_finsetSum_col (s : Finset ι) (cols : ι → ℕ → (ℕ →₀ ℂ)) (x : lpFiniteModes Conf) : dGammaOp (fun k => ∑ i ∈ s, cols i k) x = ∑ i ∈ s, dGammaOp (cols i) x

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

Preamble

-- Generated from ChapterQgCouplingDGammaSum.lean — theorem BookProof.QgCouplingDGammaSum.dGammaOp_finsetSum_col
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_ChapterNavierStokesEsa
open BookProof.FockSecondQuantization
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_finsetSum_col (s : Finset ι) (cols : ι → ℕ → (ℕ →₀ ℂ))
    (x : lpFiniteModes Conf) :
    dGammaOp (fun k => ∑ i ∈ s, cols i k) x = ∑ i ∈ s, dGammaOp (cols i) x := by sorry

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