`BookProof.FriedrichsSquare.isSelfAdjointExtension_frExt` [CompleteSpace F] (A : D →ₗ[ℂ] F) (hdense : Dense (D : Set F)) (hsym : SymmetricOn D A) (hstab : ∀ v : D, (A v : F) ∈ D) :

Proved

BookProof.FriedrichsSquare.isSelfAdjointExtension_frExt

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFriedrichsSquareFactorization.

BookProof.FriedrichsSquare.isSelfAdjointExtension_frExt [CompleteSpace F] (A : D →ₗ[ℂ] F) (hdense : Dense (D : Set F)) (hsym : SymmetricOn D A) (hstab : ∀ v : D, (A v : F) ∈ D) : IsSelfAdjointExtension (sqOp A hstab) (frExt A hdense hsym)

Formalization note: Lean 4 identifier BookProof.FriedrichsSquare.isSelfAdjointExtension_frExt.

Preamble

-- Generated from ChapterFriedrichsSquareFactorization.lean — theorem BookProof.FriedrichsSquare.isSelfAdjointExtension_frExt
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterFriedrichsSquareFactorization
import Definitions.Def_ChapterClosureUniqueness
import Definitions.Def_ChapterEsaClosureCore
import Definitions.Def_ChapterFarisLavineCore
open BookProof.ClosureUniqueness
open BookProof.EsaClosure
open BookProof.FriedrichsSquare



open BookProof.FarisLavine BookProof.EsaClosure BookProof.ClosureUniqueness

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

variable [CompleteSpace F]

Formal statement

theorem BookProof.FriedrichsSquare.isSelfAdjointExtension_frExt [CompleteSpace F] (A : D →ₗ[ℂ] F)
    (hdense : Dense (D : Set F)) (hsym : SymmetricOn D A) (hstab : ∀ v : D, (A v : F) ∈ D) :
    IsSelfAdjointExtension (sqOp A hstab) (frExt A hdense hsym) := by sorry

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