`BookProof.ChapterWeylSl2.Sl2Rep.pow_succ_apply` (T : Module.End ℂ V) (k : ℕ) (v : V) : (T ^ (k + 1)) v = T ((T ^ k) v)

Proved

BookProof.ChapterWeylSl2.Sl2Rep.pow_succ_apply

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWeylSl2.

BookProof.ChapterWeylSl2.Sl2Rep.pow_succ_apply (T : Module.End ℂ V) (k : ℕ) (v : V) : (T ^ (k + 1)) v = T ((T ^ k) v)

Formalization note: Lean 4 identifier BookProof.ChapterWeylSl2.Sl2Rep.pow_succ_apply.

Preamble

-- Generated from ChapterWeylSl2.lean — theorem BookProof.ChapterWeylSl2.Sl2Rep.pow_succ_apply
import Mathlib
import Definitions.Def_ChapterWeylSl2
open BookProof.ChapterWeylSl2
open BookProof.ChapterWeylSl2



universe u

variable {V : Type u} [AddCommGroup V] [Module ℂ V]

variable (R : Sl2Rep V)
variable {R}
variable {R : Sl2Rep V}

Formal statement

theorem BookProof.ChapterWeylSl2.Sl2Rep.pow_succ_apply (T : Module.End ℂ V) (k : ℕ) (v : V) :
    (T ^ (k + 1)) v = T ((T ^ k) v) := by sorry

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