The Lean 4 theorem `norm_sub_starProjection_antitone` in the `ChapterH9` chapter of the timepiece formalization

-- Generated from ChapterH9.lean — theorem BookProof.ChapterH9.norm_sub_starProjection_antitone
import Mathlib
import Definitions.Def_ChapterH9
open BookProof.ChapterH9


noncomputable section


open BookProof.ChapterH1 BookProof.ChapterH4 BookProof.ChapterH5 BookProof.ChapterH6
open BookProof.ChapterH8
open ContinuousLinearMap


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

theorem BookProof.ChapterH9.norm_sub_starProjection_antitone (K L : Submodule ℂ E)
    [K.HasOrthogonalProjection] [L.HasOrthogonalProjection] (hKL : K ≤ L) (v : E) :
    ‖v - L.starProjection v‖ ≤ ‖v - K.starProjection v‖ := by sorry