Theorems · Theorem · group theory
RightCancelMonoid.infinite_powers
∀ {G : Type u_1} [inst : RightCancelMonoid G] {a : G}, (↑(Submonoid.powers a)).Infinite ↔ ¬IsOfFinOrder a- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RightCancelMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coestatement · cited by 8,199
- Submonoidstatement · cited by 3,086
- Iff.notproof · cited by 489
- Submonoid.powersstatement · cited by 408
- Set.Infinitestatement · cited by 263
- IsOfFinOrderstatement · cited by 113
- RightCancelMonoidstatement and proof · cited by 18
- RightCancelMonoid.finite_powersproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- RightCancelMonoid.Nat.card_submonoidPowersproof · cited by 0