`BookProof.ClosureUniqueness.farisLavine_clGraph_eq_of_cores` {T : D →ₗ[ℂ] F} {T₁ : D₁ →ₗ[ℂ] F} {T₂ : D₂ →ₗ[ℂ] F} (h₁ : IsCoreOf T₁ T) (h₂ : IsCoreOf T₂ T) :...

Proved

BookProof.ClosureUniqueness.farisLavine_clGraph_eq_of_cores

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterClosureUniqueness.

BookProof.ClosureUniqueness.farisLavine_clGraph_eq_of_cores {T : D →ₗ[ℂ] F} {T₁ : D₁ →ₗ[ℂ] F} {T₂ : D₂ →ₗ[ℂ] F} (h₁ : IsCoreOf T₁ T) (h₂ : IsCoreOf T₂ T) : clGraph T₁ = clGraph T₂ ∧ clDom T₁ = clDom T₂ ∧ adjGraph T₁ = adjGraph T₂

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

Preamble

-- Generated from ChapterClosureUniqueness.lean — theorem BookProof.ClosureUniqueness.farisLavine_clGraph_eq_of_cores
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}

variable [CompleteSpace F]

Formal statement

theorem BookProof.ClosureUniqueness.farisLavine_clGraph_eq_of_cores {T : D →ₗ[ℂ] F} {T₁ : D₁ →ₗ[ℂ] F} {T₂ : D₂ →ₗ[ℂ] F}
    (h₁ : IsCoreOf T₁ T) (h₂ : IsCoreOf T₂ T) :
    clGraph T₁ = clGraph T₂ ∧ clDom T₁ = clDom T₂ ∧ adjGraph T₁ = adjGraph T₂ := by sorry

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