Prove2Me

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

Proved
BookProof.QgCouplingDGammaSum.quadForm_dGammaOp_finsetSum

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterQgCouplingDGammaSum.

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

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

Preamble
-- Generated from ChapterQgCouplingDGammaSum.lean — theorem BookProof.QgCouplingDGammaSum.quadForm_dGammaOp_finsetSum
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_ChapterFarisLavineCore
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.quadForm_dGammaOp_finsetSum (s : Finset ι) (cols : ι → ℕ → (ℕ →₀ ℂ))
    (x : lpFiniteModes Conf) :
    quadForm (dGammaOp (fun k => ∑ i ∈ s, cols i k)) x
      = ∑ i ∈ s, quadForm (dGammaOp (cols i)) x := by sorry

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