`BookProof.ChapterH5.krylov_subspace_span` (H : E →ₗ[K] E) (v : E) (m : ℕ) : krylovSpan H v m = Submodule.span K {x | ∃ i < m, x = (H ^ i) v}

Proved

BookProof.ChapterH5.krylov_subspace_span

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterH5.

BookProof.ChapterH5.krylov_subspace_span (H : E →ₗ[K] E) (v : E) (m : ℕ) : krylovSpan H v m = Submodule.span K {x | ∃ i < m, x = (H ^ i) v}

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

Preamble

-- Generated from ChapterH5.lean — theorem BookProof.ChapterH5.krylov_subspace_span
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}

Formal statement

theorem BookProof.ChapterH5.krylov_subspace_span (H : E →ₗ[K] E) (v : E) (m : ℕ) :
    krylovSpan H v m = Submodule.span K {x | ∃ i < m, x = (H ^ i) v} := by sorry

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