Theorems · Theorem · dynamical systems
MulAction.pow_mod_period_smul
∀ {α : Type v} {M : Type u} [inst : Monoid M] [inst_1 : MulAction M α] (n : ℕ) {m : M} {a : α},
m ^ (n % MulAction.period m a) • a = m ^ n • a- Defined in
- Mathlib.Dynamics.PeriodicPts.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- pow_addproof · cited by 315
- SemigroupAction.mul_smulproof · cited by 291
- dvd_mul_rightproof · cited by 89
- MulAction.periodstatement and proof · cited by 26
- MulAction.pow_smul_eq_iff_period_dvdproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- MulAction.pow_period_add_smulproof · cited by 0
- MulAction.pow_smul_mod_minimalPeriodproof · cited by 0
- MulAction.pow_add_period_smulproof · cited by 0