`BookProof.ClosureUniqueness.factorGraph_eq_of_clGraph_eq` {T₁ : D₁ →ₗ[ℂ] F} {T₂ : D₂ →ₗ[ℂ] F} (h : clGraph T₁ = clGraph T₂) : factorGraph T₁ = factorGraph T₂

Proved

BookProof.ClosureUniqueness.factorGraph_eq_of_clGraph_eq

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterClosureUniqueness.

BookProof.ClosureUniqueness.factorGraph_eq_of_clGraph_eq {T₁ : D₁ →ₗ[ℂ] F} {T₂ : D₂ →ₗ[ℂ] F} (h : clGraph T₁ = clGraph T₂) : factorGraph T₁ = factorGraph T₂

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

Preamble

-- Generated from ChapterClosureUniqueness.lean — theorem BookProof.ClosureUniqueness.factorGraph_eq_of_clGraph_eq
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.factorGraph_eq_of_clGraph_eq {T₁ : D₁ →ₗ[ℂ] F} {T₂ : D₂ →ₗ[ℂ] F}
    (h : clGraph T₁ = clGraph T₂) : factorGraph T₁ = factorGraph T₂ := by sorry

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