`BookProof.ClosureUniqueness.exists_isClosureOf` (T : D →ₗ[ℂ] F) (hdense : Dense (D : Set F)) (hsym : SymmetricOn D T) : ∃ (Dom : Submodule ℂ F) (A : Dom →ₗ[ℂ] F), IsClosureOf T A

Proved

BookProof.ClosureUniqueness.exists_isClosureOf

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterClosureUniqueness.

BookProof.ClosureUniqueness.exists_isClosureOf (T : D →ₗ[ℂ] F) (hdense : Dense (D : Set F)) (hsym : SymmetricOn D T) : ∃ (Dom : Submodule ℂ F) (A : Dom →ₗ[ℂ] F), IsClosureOf T A

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

Preamble

-- Generated from ChapterClosureUniqueness.lean — theorem BookProof.ClosureUniqueness.exists_isClosureOf
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.exists_isClosureOf (T : D →ₗ[ℂ] F) (hdense : Dense (D : Set F))
    (hsym : SymmetricOn D T) : ∃ (Dom : Submodule ℂ F) (A : Dom →ₗ[ℂ] F), IsClosureOf T A := by sorry

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