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Theorems · Theorem · dynamical systems

MulAction.pow_period_smul

∀ {α : Type v} {M : Type u} [inst : Monoid M] [inst_1 : MulAction M α] (m : M) (a : α), m ^ MulAction.period m a • a = a

m ^ (period m a) fixes a.

Defined in
Mathlib.Dynamics.PeriodicPts.Defs
Cited by
2 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MonoidMulAction
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MulAction.period_eq_one_iff · cited by 1MulAction.period_eq_one_i…MulAction.le_period · cited by 0MulAction.le_periodMonoid · cited by 3887MonoidMulAction · cited by 1294MulActionFunction.minimalPeriod · cited by 100Function.minimalPeriodMulAction.period · cited by 26MulAction.periodMulAction.period_eq_minimalPeriod · cited by 6MulAction.period_eq_minim…Function.iterate_minimalPeriod · cited by 3Function.iterate_minimalP…smul_iterate_apply · cited by 2smul_iterate_applyMulAction.pow_period_smulCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.