`BookProof.ChapterH5.generator_bounded_of_rankOneProjector` (u : E) (hu : ‖u‖ = 1) (D : E →L[ℂ] E) : ‖rankOneProj u + D‖ ≤ 1 + ‖D‖

Proved

BookProof.ChapterH5.generator_bounded_of_rankOneProjector

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterH5.

BookProof.ChapterH5.generator_bounded_of_rankOneProjector (u : E) (hu : ‖u‖ = 1) (D : E →L[ℂ] E) : ‖rankOneProj u + D‖ ≤ 1 + ‖D‖

Formalization note: Lean 4 identifier BookProof.ChapterH5.generator_bounded_of_rankOneProjector.

Preamble

-- Generated from ChapterH5.lean — theorem BookProof.ChapterH5.generator_bounded_of_rankOneProjector
import Mathlib
import Definitions.Def_ChapterH5
open BookProof.ChapterH5


noncomputable section



variable {K E : Type*} [Field K] [AddCommGroup E] [Module K E]

variable {H : E →ₗ[K] E} {v : E}
variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℂ E]

Formal statement

theorem BookProof.ChapterH5.generator_bounded_of_rankOneProjector (u : E) (hu : ‖u‖ = 1) (D : E →L[ℂ] E) :
    ‖rankOneProj u + D‖ ≤ 1 + ‖D‖ := by sorry

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