`BookProof.GraphCore.pushOp_apply` (U : F →ₗᵢ[ℂ] G) {D : Submodule ℂ F} (T : D →ₗ[ℂ] F) (x : pushDom U D) (x₀ : D) (hx : (x : G) = U (x₀ : F)) : pushOp U T x = U (T x₀)

Proved

BookProof.GraphCore.pushOp_apply

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGraphCoreTransfer.

BookProof.GraphCore.pushOp_apply (U : F →ₗᵢ[ℂ] G) {D : Submodule ℂ F} (T : D →ₗ[ℂ] F) (x : pushDom U D) (x₀ : D) (hx : (x : G) = U (x₀ : F)) : pushOp U T x = U (T x₀)

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

Preamble

-- Generated from ChapterGraphCoreTransfer.lean — theorem BookProof.GraphCore.pushOp_apply
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterGraphCoreTransfer
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.pushOp_apply (U : F →ₗᵢ[ℂ] G) {D : Submodule ℂ F} (T : D →ₗ[ℂ] F)
    (x : pushDom U D) (x₀ : D) (hx : (x : G) = U (x₀ : F)) :
    pushOp U T x = U (T x₀) := by sorry

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