Theorems · Theorem · group theory
AddAction.period_le_of_fixed
∀ {α : Type v} {M : Type u} [inst : AddMonoid M] [inst_1 : AddAction M α] {m : M} {a : α} {n : ℕ},
0 < n → n • m +ᵥ a = a → AddAction.period m a ≤ nIf for some n, (n • m) +ᵥ a = a, then period m a ≤ n.
- Defined in
- Mathlib.GroupTheory.GroupAction.Period
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 21 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.
- AddMonoidstatement and proof · cited by 2,864
- HVAdd.hVAddstatement and proof · cited by 1,820
- AddActionstatement and proof · cited by 820
- AddAction.periodstatement · cited by 26
- Function.IsPeriodicPt.minimalPeriod_leproof · cited by 9
- AddAction.isPeriodicPt_vadd_iffproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- AddAction.period_eq_zero_iffproof · cited by 1
- AddAction.nsmul_vadd_ne_of_lt_periodproof · cited by 0