Theorems · Theorem · dynamical systems
MulAction.zpow_mod_period_smul
∀ {α : Type v} {G : Type u} [inst : Group G] [inst_1 : MulAction G α] (j : ℤ) {g : G} {a : α},
g ^ (j % ↑(MulAction.period g a)) • a = g ^ j • a- Defined in
- Mathlib.Dynamics.PeriodicPts.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 51 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.
- Groupstatement and proof · cited by 6,238
- MulActionstatement and proof · cited by 1,294
- SemigroupAction.mul_smulproof · cited by 291
- dvd_mul_rightproof · cited by 89
- zpow_addproof · cited by 40
- MulAction.periodstatement and proof · cited by 26
- MulAction.zpow_smul_eq_iff_period_dvdproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- MulAction.zpow_smul_mod_minimalPeriodproof · cited by 2
- MulAction.zpow_add_period_smulproof · cited by 0
- MulAction.zpow_period_add_smulproof · cited by 0