Theorems · Theorem · group theory
finite_powers
∀ {G : Type u_1} [inst : LeftCancelMonoid G] {a : G}, (↑(Submonoid.powers a)).Finite ↔ IsOfFinOrder a- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LeftCancelMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coestatement and proof · cited by 8,199
- mul_oneproof · cited by 3,885
- Submonoidstatement · cited by 3,086
- LT.lt.leproof · cited by 2,189
- Set.Finitestatement and proof · cited by 1,814
- Submonoid.powersstatement and proof · cited by 408
- pow_addproof · cited by 315
- IsOfFinOrderstatement · cited by 113
- add_tsub_cancel_of_leproof · cited by 79
- LeftCancelMonoidstatement and proof · cited by 28
- isOfFinOrder_iff_pow_eq_oneproof · cited by 27
- tsub_pos_iff_ltproof · cited by 27
Cited by1
Results whose statement or proof uses this declaration.
- infinite_powersproof · cited by 1