`BookProof.VielbeinFock.inner_vielbeinDir` (d n : ℕ) (x : vielbeinSector d n) (j : Fin n) (i : Fin (d + 1)) : (inner ℝ x (vielbeinDir d n j i) : ℝ) = x (j, i)

Proved

BookProof.VielbeinFock.inner_vielbeinDir

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterVielbeinFiberFock.

BookProof.VielbeinFock.inner_vielbeinDir (d n : ℕ) (x : vielbeinSector d n) (j : Fin n) (i : Fin (d + 1)) : (inner ℝ x (vielbeinDir d n j i) : ℝ) = x (j, i)

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

Preamble

-- Generated from ChapterVielbeinFiberFock.lean — theorem BookProof.VielbeinFock.inner_vielbeinDir
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.inner_vielbeinDir (d n : ℕ) (x : vielbeinSector d n) (j : Fin n) (i : Fin (d + 1)) :
    (inner ℝ x (vielbeinDir d n j i) : ℝ) = x (j, i) := by sorry

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