Prove2Me

`BookProof.GraphCore.symmetricOn_restrictOp` {D₁ D₂ : Submodule ℂ F} (T : D₂ →ₗ[ℂ] F) (h : D₁ ≤ D₂) (hT : SymmetricOn D₂ T) : SymmetricOn D₁ (restrictOp T h)

Proved
BookProof.GraphCore.symmetricOn_restrictOp

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGraphCoreTransfer.

BookProof.GraphCore.symmetricOn_restrictOp {D₁ D₂ : Submodule ℂ F} (T : D₂ →ₗ[ℂ] F) (h : D₁ ≤ D₂) (hT : SymmetricOn D₂ T) : SymmetricOn D₁ (restrictOp T h)

Formalization note: Lean 4 identifier BookProof.GraphCore.symmetricOn_restrictOp.

Preamble
-- Generated from ChapterGraphCoreTransfer.lean — theorem BookProof.GraphCore.symmetricOn_restrictOp
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterGraphCoreTransfer
import Definitions.Def_ChapterFarisLavineCore
open BookProof.GraphCore



open BookProof.FarisLavine

variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F]
Formal statement
theorem BookProof.GraphCore.symmetricOn_restrictOp {D₁ D₂ : Submodule ℂ F} (T : D₂ →ₗ[ℂ] F) (h : D₁ ≤ D₂)
    (hT : SymmetricOn D₂ T) : SymmetricOn D₁ (restrictOp T h) := by sorry

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