Prove2Me

`BookProof.ChapterSchurIrreducible.rangeClosure_ne_bot` {F : V →L[ℂ] V} (hF : F ≠ 0) : rangeClosure F ≠ ⊥

Proved
BookProof.ChapterSchurIrreducible.rangeClosure_ne_bot

by leonardopedro · Oct 17, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSchurIrreducible.

BookProof.ChapterSchurIrreducible.rangeClosure_ne_bot {F : V →L[ℂ] V} (hF : F ≠ 0) : rangeClosure F ≠ ⊥

Formalization note: Lean 4 identifier BookProof.ChapterSchurIrreducible.rangeClosure_ne_bot.

Preamble
-- Generated from ChapterSchurIrreducible.lean — theorem BookProof.ChapterSchurIrreducible.rangeClosure_ne_bot
import Definitions.Def_ChapterA
import Mathlib
import Definitions.Def_ChapterSchurIrreducible
open BookProof.ChapterSchurIrreducible


open scoped ComplexConjugate InnerProductSpace


open BookProof.ChapterA BookProof.ChapterA.System

variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℂ V] [CompleteSpace V]
Formal statement
theorem BookProof.ChapterSchurIrreducible.rangeClosure_ne_bot {F : V →L[ℂ] V} (hF : F ≠ 0) : rangeClosure F ≠ ⊥ := by sorry

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