Prove2Me

`BookProof.ClosureUniqueness.opGraph_clExt` (T : D →ₗ[ℂ] F) (hdense : Dense (D : Set F)) (hsym : SymmetricOn D T) : opGraph (clExt T hdense hsym) = clGraph T

Proved
BookProof.ClosureUniqueness.opGraph_clExt

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterClosureUniqueness.

BookProof.ClosureUniqueness.opGraph_clExt (T : D →ₗ[ℂ] F) (hdense : Dense (D : Set F)) (hsym : SymmetricOn D T) : opGraph (clExt T hdense hsym) = clGraph T

Formalization note: Lean 4 identifier BookProof.ClosureUniqueness.opGraph_clExt.

Preamble
-- Generated from ChapterClosureUniqueness.lean — theorem BookProof.ClosureUniqueness.opGraph_clExt
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterClosureUniqueness
import Definitions.Def_ChapterEsaClosureCore
import Definitions.Def_ChapterFarisLavineCore
open BookProof.EsaClosure
open BookProof.ClosureUniqueness



open BookProof.FarisLavine BookProof.EsaClosure

variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F]
variable {D D₁ D₂ Dom Dom₁ Dom₂ : Submodule ℂ F}
Formal statement
theorem BookProof.ClosureUniqueness.opGraph_clExt (T : D →ₗ[ℂ] F) (hdense : Dense (D : Set F)) (hsym : SymmetricOn D T) :
    opGraph (clExt T hdense hsym) = clGraph T := by sorry

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