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Theorems · Theorem · group theory

AddAction.period_pos_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 → 0 < AddAction.period m a

If for some n, (n • m) +ᵥ a = a, then 0 < period m a.

Defined in
Mathlib.GroupTheory.GroupAction.Period
Cited by
1 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddMonoidAddAction
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Around this declaration

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AddAction.period_eq_zero_iff · cited by 1AddAction.period_eq_zero_…AddMonoid · cited by 2864AddMonoidHVAdd.hVAdd · cited by 1820HVAdd.hVAddAddAction · cited by 820AddActionAddAction.period · cited by 26AddAction.periodFunction.IsPeriodicPt.minimalPeriod_pos · cited by 6IsPeriodicPt.minimalPerio…AddAction.isPeriodicPt_vadd_iff · cited by 4AddAction.isPeriodicPt_va…AddAction.period_pos_of_fixedCITED BYCITES

Cites6

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Cited by1

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