`BookProof.VielbeinFock.shearEnergy_apply` (d : ℕ) (om : Fin d → ℝ) (n : ℕ) (j : Fin n) (x : vielbeinSector d n) : shearEnergy d om n j x = ∑ i : Fin d, om i ^ 2 / 2 * (x (j, i.cas

Proved

BookProof.VielbeinFock.shearEnergy_apply

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterVielbeinFiberFock.

BookProof.VielbeinFock.shearEnergy_apply (d : ℕ) (om : Fin d → ℝ) (n : ℕ) (j : Fin n) (x : vielbeinSector d n) : shearEnergy d om n j x = ∑ i : Fin d, om i ^ 2 / 2 * (x (j, i.castSucc)) ^ 2

Formalization note: Lean 4 identifier BookProof.VielbeinFock.shearEnergy_apply.

Preamble

-- Generated from ChapterVielbeinFiberFock.lean — theorem BookProof.VielbeinFock.shearEnergy_apply
import Definitions.Def_ChapterStarobinskyPotential
import Definitions.Def_ChapterScalaronCoreEsa
import Definitions.Def_ChapterScalaronFockEsa
import Definitions.Def_ChapterDirectSumEsa
import Definitions.Def_ChapterStoneBridge
import Definitions.Def_ChapterEsaClosureCore
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterSirkTrotterKato
import Mathlib
import Definitions.Def_ChapterVielbeinFiberFock
open BookProof.VielbeinFock


open Filter Topology MeasureTheory


open BookProof.Starobinsky BookProof.ScalaronEsa BookProof.ScalaronFock
open BookProof.DirectSumEsa BookProof.StoneBridge BookProof.EsaClosure
open BookProof.FarisLavine BookProof.ChapterStoneResolvent

noncomputable section

Formal statement

theorem BookProof.VielbeinFock.shearEnergy_apply (d : ℕ) (om : Fin d → ℝ) (n : ℕ) (j : Fin n)
    (x : vielbeinSector d n) :
    shearEnergy d om n j x = ∑ i : Fin d, om i ^ 2 / 2 * (x (j, i.castSucc)) ^ 2 := by sorry

View graph