The Lean 4 theorem `weylOpDom_quadForm` in the `ChapterYangMillsFriedrichs` chapter of the timepiece formalization

Proved

BookProof.YangMillsFriedrichs.weylOpDom_quadForm_inc

by leonardopedro · Oct 17, 2026 · Mathlib 0df444a (Lean v4.33.1)

timepiece

The Lean 4 theorem weylOpDom_quadForm in the ChapterYangMillsFriedrichs chapter of the timepiece formalization.

Replaces the unuploadable node BookProof_YangMillsFriedrichs_weylOpDom_quadForm, whose statement name is already declared inside its published definition bundle; the _inc suffix publishes the same statement as its own node.

Preamble

-- Generated from ChapterYangMillsFriedrichs.lean — theorem BookProof.YangMillsFriedrichs.weylOpDom_quadForm_inc
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterYangMillsFriedrichs
import Definitions.Def_ChapterFarisLavineCore
open BookProof.YangMillsFriedrichs



open BookProof.FarisLavine



variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F] {D : Submodule ℂ F}

Formal statement

theorem BookProof.YangMillsFriedrichs.weylOpDom_quadForm_inc {n m : ℕ} {pi : Fin n → D →ₗ[ℂ] D} {Bf : Fin m → D →ₗ[ℂ] D}
    (hpi : ∀ i, SymmetricOn D (D.subtype.comp (pi i)))
    (hB : ∀ a, SymmetricOn D (D.subtype.comp (Bf a))) (x : D) :
    quadForm (weylOp pi Bf) x
      = 1 / 2 * (∑ i, ‖((pi i x : D) : F)‖ ^ 2) + 1 / 2 * ∑ a, ‖((Bf a x : D) : F)‖ ^ 2 := by sorry

Source

https://github.com/leonardopedro/timepiece/blob/61595bc/BookProof/ChapterYangMillsFriedrichs.lean

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