`BookProof.YangMillsAbelianNoGap.facS_pos` (j : Fin d) : 0 < facS vf Mf j

Proved

BookProof.YangMillsAbelianNoGap.facS_pos

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterYangMillsAbelianNoGap.

BookProof.YangMillsAbelianNoGap.facS_pos (j : Fin d) : 0 < facS vf Mf j

Formalization note: Lean 4 identifier BookProof.YangMillsAbelianNoGap.facS_pos.

Preamble

-- Generated from ChapterYangMillsAbelianNoGap.lean — theorem BookProof.YangMillsAbelianNoGap.facS_pos
import Definitions.Def_ChapterHermiteProductCore
import Definitions.Def_ChapterYangMillsHermite
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterHermiteGalerkinFriedrichs
import Mathlib
import Definitions.Def_ChapterYangMillsAbelianNoGap
import Definitions.Def_ChapterGaussCoordCombo
import Definitions.Def_ChapterSqueezedGaussStates
open BookProof.GaussCoordCombo
open BookProof.SqueezedGaussStates
open BookProof.YangMillsAbelianNoGap



open MvPolynomial MeasureTheory
open BookProof.HermiteProductCore BookProof.GaussCoordCombo BookProof.SqueezedGaussStates
open BookProof.YangMillsHermite BookProof.FarisLavine BookProof.HermiteGalerkin

noncomputable section

variable {d : ℕ}

variable (vf : Fin d → ℝ) (Mf : Fin d → ℕ)

Formal statement

theorem BookProof.YangMillsAbelianNoGap.facS_pos (j : Fin d) : 0 < facS vf Mf j := by sorry

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