`BookProof.ClosureUniqueness.clGraph_le_opGraph_of_isClosedExtension` {T : D →ₗ[ℂ] F} {A : Dom →ₗ[ℂ] F} (h : IsClosedExtension T A) : clGraph T ≤ opGraph A

Proved

BookProof.ClosureUniqueness.clGraph_le_opGraph_of_isClosedExtension

by leonardopedro · Oct 11, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterClosureUniqueness.

BookProof.ClosureUniqueness.clGraph_le_opGraph_of_isClosedExtension {T : D →ₗ[ℂ] F} {A : Dom →ₗ[ℂ] F} (h : IsClosedExtension T A) : clGraph T ≤ opGraph A

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

Preamble

-- Generated from ChapterClosureUniqueness.lean — theorem BookProof.ClosureUniqueness.clGraph_le_opGraph_of_isClosedExtension
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterClosureUniqueness
import Definitions.Def_ChapterEsaClosureCore
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.clGraph_le_opGraph_of_isClosedExtension {T : D →ₗ[ℂ] F} {A : Dom →ₗ[ℂ] F}
    (h : IsClosedExtension T A) : clGraph T ≤ opGraph A := by sorry

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