`BookProof.GraphCore.IsGraphCore.trans` {D₁ D₂ D₃ : Submodule ℂ F} {T : D₃ →ₗ[ℂ] F} (h₂₃ : D₂ ≤ D₃) (h₁ : IsGraphCore D₁ (restrictOp T h₂₃)) (h₂ : IsGraphCore...

Proved

BookProof.GraphCore.IsGraphCore.trans

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGraphCoreTransfer.

BookProof.GraphCore.IsGraphCore.trans {D₁ D₂ D₃ : Submodule ℂ F} {T : D₃ →ₗ[ℂ] F} (h₂₃ : D₂ ≤ D₃) (h₁ : IsGraphCore D₁ (restrictOp T h₂₃)) (h₂ : IsGraphCore D₂ T) : IsGraphCore D₁ T

Formalization note: Lean 4 identifier BookProof.GraphCore.IsGraphCore.trans.

Preamble

-- Generated from ChapterGraphCoreTransfer.lean — theorem BookProof.GraphCore.IsGraphCore.trans
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterGraphCoreTransfer
open BookProof.GraphCore



open BookProof.FarisLavine

variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F]

Formal statement

theorem BookProof.GraphCore.IsGraphCore.trans {D₁ D₂ D₃ : Submodule ℂ F} {T : D₃ →ₗ[ℂ] F}
    (h₂₃ : D₂ ≤ D₃) (h₁ : IsGraphCore D₁ (restrictOp T h₂₃)) (h₂ : IsGraphCore D₂ T) :
    IsGraphCore D₁ T := by sorry

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