Theorems · Theorem · dynamical systems
AddAction.zsmul_vadd_eq_iff_period_dvd
∀ {α : Type v} {G : Type u} [inst : AddGroup G] [inst_1 : AddAction G α] {j : ℤ} {g : G} {a : α},
j • g +ᵥ a = a ↔ ↑(AddAction.period g a) ∣ j- Defined in
- Mathlib.Dynamics.PeriodicPts.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 50 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- HVAdd.hVAddstatement and proof · cited by 1,820
- AddActionstatement and proof · cited by 820
- natCast_zsmulproof · cited by 118
- neg_zsmulproof · cited by 41
- AddAction.periodstatement and proof · cited by 26
- neg_vadd_eq_iffproof · cited by 13
- AddAction.nsmul_vadd_eq_iff_period_dvdproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- AddAction.zsmul_mod_period_vaddproof · cited by 3
- AddAction.zsmul_vadd_eq_iff_minimalPeriod_dvdproof · cited by 1