Theorems · Theorem · group theory
RightCancelMonoid.Nat.card_submonoidPowers
∀ {G : Type u_1} [inst : RightCancelMonoid G] {a : G}, Nat.card ↥(Submonoid.powers a) = orderOf aSee also orderOf_eq_card_powers.
- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RightCancelMonoid
Around this declaration
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Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coeproof · cited by 8,199
- Set.Elemproof · cited by 7,166
- Equiv.symmproof · cited by 3,681
- Submonoidstatement · cited by 3,086
- Nat.cardstatement and proof · cited by 844
- Submonoid.powersstatement and proof · cited by 408
- Infiniteproof · cited by 352
- orderOfstatement and proof · cited by 324
- Fintype.card_finproof · cited by 270
- Nat.card_eq_fintype_cardproof · cited by 200
- Nat.card_congrproof · cited by 133
- IsOfFinOrderproof · cited by 113
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