`BookProof.FockNumberPreservingGap.shiftCol_apply` (col : ℕ → (ℕ →₀ ℂ)) (mu : ℝ) (k : ℕ) : shiftCol col mu k = col k - ((mu : ℝ) : ℂ) • numberCol k

Proved

BookProof.FockNumberPreservingGap.shiftCol_apply

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFockNumberPreservingGap.

BookProof.FockNumberPreservingGap.shiftCol_apply (col : ℕ → (ℕ →₀ ℂ)) (mu : ℝ) (k : ℕ) : shiftCol col mu k = col k - ((mu : ℝ) : ℂ) • numberCol k

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

Preamble

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


noncomputable section


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

Formal statement

theorem BookProof.FockNumberPreservingGap.shiftCol_apply (col : ℕ → (ℕ →₀ ℂ)) (mu : ℝ) (k : ℕ) :
    shiftCol col mu k = col k - ((mu : ℝ) : ℂ) • numberCol k := by sorry

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