`BookProof.ReducedEsa.commutes_asymProj` {hUD : ∀ x ∈ D, U x ∈ D} (hTU : ∀ x : D, T ⟨U (x : F), hUD _ x.2⟩ = U (T x)) : Commutes T (asymProj_mem (D := D) hUD) where comm x

Proved

BookProof.ReducedEsa.commutes_asymProj

by leonardopedro · Oct 11, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterReducingSubspaceEsa.

BookProof.ReducedEsa.commutes_asymProj {hUD : ∀ x ∈ D, U x ∈ D} (hTU : ∀ x : D, T ⟨U (x : F), hUD _ x.2⟩ = U (T x)) : Commutes T (asymProj_mem (D := D) hUD) where comm x

Formalization note: Lean 4 identifier BookProof.ReducedEsa.commutes_asymProj.

Preamble

-- Generated from ChapterReducingSubspaceEsa.lean — theorem BookProof.ReducedEsa.commutes_asymProj
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterGraphCoreTransfer
import Mathlib
import Definitions.Def_ChapterReducingSubspaceEsa
import Definitions.Def_ChapterA
import Theorems.Thm_BookProof_ReducedEsa_asymProj_mem
open BookProof.ChapterA
open BookProof.ChapterA.System
open BookProof.ReducedEsa



open BookProof.FarisLavine BookProof.GraphCore

noncomputable section

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

variable {P : F →ₗ[ℂ] F}
variable {D : Submodule ℂ F}
variable (T : D →ₗ[ℂ] F)
variable {T}
variable (U : F →ₗ[ℂ] F)
variable {U}

Formal statement

theorem BookProof.ReducedEsa.commutes_asymProj {hUD : ∀ x ∈ D, U x ∈ D}
    (hTU : ∀ x : D, T ⟨U (x : F), hUD _ x.2⟩ = U (T x)) :
    Commutes T (asymProj_mem (D := D) hUD) where
  comm x := by sorry

View graph