`BookProof.ChapterH5.inversion_free_seed` (S R : E →ₗ[K] E) (v₀ : E) (m : ℕ) (hR : R.comp S = LinearMap.id) : R ((S ^ (m + 1)) v₀) = (S ^ m) v₀

Proved

BookProof.ChapterH5.inversion_free_seed

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterH5.

BookProof.ChapterH5.inversion_free_seed (S R : E →ₗ[K] E) (v₀ : E) (m : ℕ) (hR : R.comp S = LinearMap.id) : R ((S ^ (m + 1)) v₀) = (S ^ m) v₀

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

Preamble

-- Generated from ChapterH5.lean — theorem BookProof.ChapterH5.inversion_free_seed
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.inversion_free_seed (S R : E →ₗ[K] E) (v₀ : E) (m : ℕ)
    (hR : R.comp S = LinearMap.id) :
    R ((S ^ (m + 1)) v₀) = (S ^ m) v₀ := by sorry

View graph