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Theorems · Theorem · group theory

MulAction.period_eq_one_iff

∀ {α : Type v} {M : Type u} [inst : Monoid M] [inst_1 : MulAction M α] {m : M} {a : α},
  MulAction.period m a = 1 ↔ m • a = a
Defined in
Mathlib.GroupTheory.GroupAction.Period
Cited by
1 results in Mathlib
Foundations
Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MonoidMulAction
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Around this declaration

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

MulAction.period_one · cited by 0MulAction.period_oneMonoid · cited by 3887Monoidle_antisymm · cited by 2068le_antisymmMulAction · cited by 1294MulActionpow_one · cited by 894pow_oneone_pos · cited by 102one_posMulAction.period · cited by 26MulAction.periodMulAction.period_le_of_fixed · cited by 2MulAction.period_le_of_fi…MulAction.pow_period_smul · cited by 2MulAction.pow_period_smulMulAction.period_pos_of_fixed · cited by 1MulAction.period_pos_of_f…MulAction.period_eq_one_iffCITED BYCITES

Cites9

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Cited by1

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