`BookProof.GraphCore.pushDom_mono` (U : F →ₗᵢ[ℂ] G) {D₁ D₂ : Submodule ℂ F} (h : D₁ ≤ D₂) : pushDom U D₁ ≤ pushDom U D₂

Proved

BookProof.GraphCore.pushDom_mono

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGraphCoreTransfer.

BookProof.GraphCore.pushDom_mono (U : F →ₗᵢ[ℂ] G) {D₁ D₂ : Submodule ℂ F} (h : D₁ ≤ D₂) : pushDom U D₁ ≤ pushDom U D₂

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

Preamble

-- Generated from ChapterGraphCoreTransfer.lean — theorem BookProof.GraphCore.pushDom_mono
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.pushDom_mono (U : F →ₗᵢ[ℂ] G) {D₁ D₂ : Submodule ℂ F} (h : D₁ ≤ D₂) :
    pushDom U D₁ ≤ pushDom U D₂ := by sorry

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