`BookProof.FockNumberPreservingGap.creVec_eq_sum_of_subset` (v : ℕ →₀ ℂ) (x : FockAlg) {s : Finset ℕ} (h : v.support ⊆ s) : creVec v x = ∑ j ∈ s, v j • creA j x

Proved

BookProof.FockNumberPreservingGap.creVec_eq_sum_of_subset

by leonardopedro · Oct 5, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFockNumberPreservingGap.

BookProof.FockNumberPreservingGap.creVec_eq_sum_of_subset (v : ℕ →₀ ℂ) (x : FockAlg) {s : Finset ℕ} (h : v.support ⊆ s) : creVec v x = ∑ j ∈ s, v j • creA j x

Formalization note: Lean 4 identifier BookProof.FockNumberPreservingGap.creVec_eq_sum_of_subset.

Preamble

-- Generated from ChapterFockNumberPreservingGap.lean — theorem BookProof.FockNumberPreservingGap.creVec_eq_sum_of_subset
import Definitions.Def_ChapterFockOneParticleGap
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Mathlib
import Definitions.Def_ChapterFockNumberPreservingGap
import Definitions.Def_ChapterFockSecondQuantization
open BookProof.FockSecondQuantization
open BookProof.FockNumberPreservingGap


noncomputable section


open BookProof.FockSecondQuantization BookProof.FockOneParticleGap
open BookProof.FarisLavine BookProof.NavierStokesFlow

Formal statement

theorem BookProof.FockNumberPreservingGap.creVec_eq_sum_of_subset (v : ℕ →₀ ℂ) (x : FockAlg) {s : Finset ℕ}
    (h : v.support ⊆ s) : creVec v x = ∑ j ∈ s, v j • creA j x := by sorry

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