Theorems · Theorem · group theory
IsOfFinOrder.finite_powers
∀ {G : Type u_1} [inst : Monoid G] {a : G}, IsOfFinOrder a → (↑(Submonoid.powers a)).Finite- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- SetLike.coestatement · cited by 8,199
- Monoidstatement and proof · cited by 3,887
- Submonoidstatement · cited by 3,086
- Set.Finitestatement and proof · cited by 1,814
- Finset.rangeproof · cited by 1,341
- Finset.imageproof · cited by 910
- Submonoid.powersstatement · cited by 408
- orderOfproof · cited by 324
- Finset.finite_toSetproof · cited by 210
- IsOfFinOrderstatement and proof · cited by 113
- IsOfFinOrder.powers_eq_image_range_orderOfproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Monoid.finite_set_isOfFiniteOrder_of_descentproof · cited by 1
- RightCancelMonoid.finite_powersproof · cited by 1
- finite_powersproof · cited by 1