`BookProof.QgCouplingDGammaSum.creVec_eq_sum` {v : ℕ →₀ ℂ} {L : Finset ℕ} (hL : v.support ⊆ L) (x : FockAlg) : creVec v x = ∑ j ∈ L, v j • creA j x

Proved

BookProof.QgCouplingDGammaSum.creVec_eq_sum

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterQgCouplingDGammaSum.

BookProof.QgCouplingDGammaSum.creVec_eq_sum {v : ℕ →₀ ℂ} {L : Finset ℕ} (hL : v.support ⊆ L) (x : FockAlg) : creVec v x = ∑ j ∈ L, v j • creA j x

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

Preamble

-- Generated from ChapterQgCouplingDGammaSum.lean — theorem BookProof.QgCouplingDGammaSum.creVec_eq_sum
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
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.creVec_eq_sum {v : ℕ →₀ ℂ} {L : Finset ℕ} (hL : v.support ⊆ L) (x : FockAlg) :
    creVec v x = ∑ j ∈ L, v j • creA j x := by sorry

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