`BookProof.FriedrichsCanonical.qgScalaronPosSymOp_dense` (M alpha : ℝ) (hM : 0 < M) (halpha : 0 < alpha) : Dense (((qgScalaronPosSymOp M alpha hM halpha).dom : Submodule ℂ (L2d 1))

Proved

BookProof.FriedrichsCanonical.qgScalaronPosSymOp_dense

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFriedrichsCanonical.

BookProof.FriedrichsCanonical.qgScalaronPosSymOp_dense (M alpha : ℝ) (hM : 0 < M) (halpha : 0 < alpha) : Dense (((qgScalaronPosSymOp M alpha hM halpha).dom : Submodule ℂ (L2d 1)) : Set (L2d 1))

Formalization note: Lean 4 identifier BookProof.FriedrichsCanonical.qgScalaronPosSymOp_dense.

Preamble

-- Generated from ChapterFriedrichsCanonical.lean — theorem BookProof.FriedrichsCanonical.qgScalaronPosSymOp_dense
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterYangMillsFriedrichs
import Definitions.Def_ChapterComplexShiftCore
import Definitions.Def_ChapterFriedrichsExtension
import Mathlib
import Definitions.Def_ChapterFriedrichsCanonical
import Definitions.Def_ChapterHermiteProductCore
open BookProof.HermiteProductCore
open BookProof.FriedrichsCanonical



open BookProof.FarisLavine BookProof.YangMillsFriedrichs BookProof.HashimotoShiftInvert
open BookProof.FriedrichsExtension BookProof.FriedrichsExtension.FormDom

noncomputable section

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

variable {D : Submodule ℂ F}

Formal statement

theorem BookProof.FriedrichsCanonical.qgScalaronPosSymOp_dense (M alpha : ℝ) (hM : 0 < M) (halpha : 0 < alpha) :
    Dense (((qgScalaronPosSymOp M alpha hM halpha).dom : Submodule ℂ (L2d 1)) : Set (L2d 1)) := by sorry

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