Theorems · Theorem · dynamical systems
MulAction.pow_smul_eq_iff_period_dvd
∀ {α : Type v} {M : Type u} [inst : Monoid M] [inst_1 : MulAction M α] {n : ℕ} {m : M} {a : α},
m ^ n • a = a ↔ MulAction.period m a ∣ n- Defined in
- Mathlib.Dynamics.PeriodicPts.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- MulActionstatement and proof · cited by 1,294
- MulAction.periodstatement · cited by 26
- MulAction.period_eq_minimalPeriodproof · cited by 6
- Function.isPeriodicPt_iff_minimalPeriod_dvdproof · cited by 6
- MulAction.isPeriodicPt_smul_iffproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- MulAction.pow_mod_period_smulproof · cited by 3
- MulAction.zpow_smul_eq_iff_period_dvdproof · cited by 2
- MulAction.period_dvd_exponentproof · cited by 2
- MulAction.period_dvd_orderOfproof · cited by 2
- MulAction.pow_smul_eq_iff_minimalPeriod_dvdproof · cited by 1