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Theorems · Theorem · group theory

AddAction.period_eq_zero_iff

∀ {α : Type v} {M : Type u} [inst : AddMonoid M] [inst_1 : AddAction M α] {m : M} {a : α},
  AddAction.period m a = 1 ↔ m +ᵥ 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
AddMonoidAddAction
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Around this declaration

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

AddAction.period_zero · cited by 0AddAction.period_zeroAddMonoid · cited by 2864AddMonoidle_antisymm · cited by 2068le_antisymmHVAdd.hVAdd · cited by 1820HVAdd.hVAddAddAction · cited by 820AddActionone_pos · cited by 102one_posone_nsmul · cited by 63one_nsmulAddAction.period · cited by 26AddAction.periodAddAction.nsmul_period_vadd · cited by 2AddAction.nsmul_period_va…AddAction.period_le_of_fixed · cited by 2AddAction.period_le_of_fi…AddAction.period_pos_of_fixed · cited by 1AddAction.period_pos_of_f…AddAction.period_eq_zero_iffCITED BYCITES

Cites10

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Cited by1

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