Prove2Me

`BookProof.QuantumGravityFock.ghostEnergy_insert` {g : ℕ → ℝ} {a : ℕ} {α : FermConf} (h : a ∉ α) : ghostEnergy g (insert a α) = g a + ghostEnergy g α

Proved
BookProof.QuantumGravityFock.ghostEnergy_insert

by leonardopedro · Oct 16, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterQuantumGravityFock.

BookProof.QuantumGravityFock.ghostEnergy_insert {g : ℕ → ℝ} {a : ℕ} {α : FermConf} (h : a ∉ α) : ghostEnergy g (insert a α) = g a + ghostEnergy g α

Formalization note: Lean 4 identifier BookProof.QuantumGravityFock.ghostEnergy_insert.

Preamble
-- Generated from ChapterQuantumGravityFock.lean — theorem BookProof.QuantumGravityFock.ghostEnergy_insert
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Definitions.Def_ChapterNavierStokesIkebeKato
import Definitions.Def_ChapterNavierStokesFockSpace
import Definitions.Def_ChapterNavierStokesFullEsa
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterStoneBridge
import Definitions.Def_ChapterEsaClosureCore
import Definitions.Def_ChapterSirkTrotterKato
import Definitions.Def_ChapterYangMillsFriedrichs
import Definitions.Def_ChapterHermiteGalerkinFriedrichs
import Definitions.Def_ChapterComplexShiftCore
import Definitions.Def_ChapterFockSecondQuantization
import Mathlib
import Definitions.Def_ChapterQuantumGravityFock
import Definitions.Def_ChapterYangMillsGhostSector
open BookProof.YangMillsGhost
open BookProof.QuantumGravityFock



open BookProof.NavierStokesFlow BookProof.NavierStokesFlow.IkebeKato
open BookProof.NavierStokesFlow.FockOfFock BookProof.NavierStokesFlow.FullEsa
open BookProof.FarisLavine BookProof.StoneBridge BookProof.EsaClosure
open BookProof.ChapterStoneResolvent BookProof.YangMillsFriedrichs
open BookProof.HermiteGalerkin BookProof.HashimotoShiftInvert
open BookProof.FockSecondQuantization

noncomputable section
Formal statement
theorem BookProof.QuantumGravityFock.ghostEnergy_insert {g : ℕ → ℝ} {a : ℕ} {α : FermConf} (h : a ∉ α) :
    ghostEnergy g (insert a α) = g a + ghostEnergy g α := by sorry

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