`BookProof.ChapterH7.compression_rayleigh_real` (V : F →L[ℂ] E) (X : E →L[ℂ] E) (hX : IsSelfAdjoint X) (y : F) : (inner ℂ y (compress V X y) : ℂ).im = 0

Proved

BookProof.ChapterH7.compression_rayleigh_real

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterH7.

BookProof.ChapterH7.compression_rayleigh_real (V : F →L[ℂ] E) (X : E →L[ℂ] E) (hX : IsSelfAdjoint X) (y : F) : (inner ℂ y (compress V X y) : ℂ).im = 0

Formalization note: Lean 4 identifier BookProof.ChapterH7.compression_rayleigh_real.

Preamble

-- Generated from ChapterH7.lean — theorem BookProof.ChapterH7.compression_rayleigh_real
import Definitions.Def_ChapterH6
import Mathlib
import Definitions.Def_ChapterH7
import Definitions.Def_ChapterH4
open BookProof.ChapterH4
open BookProof.ChapterH7


noncomputable section

open BookProof.ChapterH4 BookProof.ChapterH6

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

Formal statement

theorem BookProof.ChapterH7.compression_rayleigh_real (V : F →L[ℂ] E) (X : E →L[ℂ] E)
    (hX : IsSelfAdjoint X) (y : F) : (inner ℂ y (compress V X y) : ℂ).im = 0 := by sorry

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