`BookProof.ChapterSchurIrreducible.rangeClosure_le_ker` {F G : V →L[ℂ] V} (h : G * F = 0) : rangeClosure F ≤ LinearMap.ker (G : V →ₗ[ℂ] V)

Proved

BookProof.ChapterSchurIrreducible.rangeClosure_le_ker

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSchurIrreducible.

BookProof.ChapterSchurIrreducible.rangeClosure_le_ker {F G : V →L[ℂ] V} (h : G * F = 0) : rangeClosure F ≤ LinearMap.ker (G : V →ₗ[ℂ] V)

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

Preamble

-- Generated from ChapterSchurIrreducible.lean — theorem BookProof.ChapterSchurIrreducible.rangeClosure_le_ker
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_le_ker {F G : V →L[ℂ] V} (h : G * F = 0) :
    rangeClosure F ≤ LinearMap.ker (G : V →ₗ[ℂ] V) := by sorry

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