le_period — Mathlib

English

If Hk is IsMultiplyPretransitive G α k, then (fixingSubgroup G s).index · (|α| − k)! = |α|!.

Русский

Если Hk = IsMultiplyPretransitive G α k, то индекс fixingSubgroup G s умножить на (|α| − k)! равно |α|!.

LaTeX

$$(fixingSubgroup G s).index · (|α| - s.ncard)! = |α|!$$

Lean4

/-- If the action is periodic, then a lower bound for its period can be computed. -/
@[to_additive /-- If the action is periodic, then a lower bound for its period can be computed. -/
    ]
theorem le_period {m : M} {a : α} {n : ℕ} (period_pos : 0 < period m a) (moved : ∀ k, 0 < k → k < n → m ^ k • a ≠ a) :
    n ≤ period m a :=
  le_of_not_gt fun period_lt_n => moved _ period_pos period_lt_n <| pow_period_smul m a

Похожие утверждения