Prove2Me

`BookProof.GraphCore.symmetricOn_pushOp` (U : F →ₗᵢ[ℂ] G) {D : Submodule ℂ F} (T : D →ₗ[ℂ] F) (hT : SymmetricOn D T) : SymmetricOn (pushDom U D) (pushOp U T)

Proved
BookProof.GraphCore.symmetricOn_pushOp

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGraphCoreTransfer.

BookProof.GraphCore.symmetricOn_pushOp (U : F →ₗᵢ[ℂ] G) {D : Submodule ℂ F} (T : D →ₗ[ℂ] F) (hT : SymmetricOn D T) : SymmetricOn (pushDom U D) (pushOp U T)

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

Preamble
-- Generated from ChapterGraphCoreTransfer.lean — theorem BookProof.GraphCore.symmetricOn_pushOp
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]

variable {G : Type*} [NormedAddCommGroup G] [InnerProductSpace ℂ G]
Formal statement
theorem BookProof.GraphCore.symmetricOn_pushOp (U : F →ₗᵢ[ℂ] G) {D : Submodule ℂ F} (T : D →ₗ[ℂ] F)
    (hT : SymmetricOn D T) : SymmetricOn (pushDom U D) (pushOp U T) := by sorry

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