Theorems · Theorem · group theory
IsOfFinOrder.natCard_powers_le_orderOf
∀ {G : Type u_1} [inst : Monoid G] {a : G}, IsOfFinOrder a → Nat.card ↑↑(Submonoid.powers a) ≤ orderOf a- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Monoid
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Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coestatement · cited by 8,199
- Set.Elemstatement and proof · cited by 7,166
- Set.imageproof · cited by 5,609
- Monoidstatement and proof · cited by 3,887
- Submonoidstatement · cited by 3,086
- Finset.cardproof · cited by 2,327
- Finset.rangeproof · cited by 1,341
- Set.Iioproof · cited by 1,166
- Finset.imageproof · cited by 910
- Nat.cardstatement and proof · cited by 844
- Submonoid.powersstatement · cited by 408
- orderOfstatement and proof · cited by 324
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