Theorems · Theorem · group theory
Nat.card_addSubmonoidMultiples
∀ {G : Type u_1} [inst : AddLeftCancelMonoid G] {a : G}, Nat.card ↥(AddSubmonoid.multiples a) = addOrderOf aSee also addOrder_eq_card_multiples.
- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddLeftCancelMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- AddSubmonoidstatement · cited by 1,178
- Nat.cardstatement and proof · cited by 844
- Infiniteproof · cited by 352
- Fintype.card_finproof · cited by 270
- addOrderOfstatement and proof · cited by 208
- Nat.card_eq_fintype_cardproof · cited by 200
- Nat.card_congrproof · cited by 133
- IsOfFinAddOrderproof · cited by 105
- Nat.card_eq_zero_of_infiniteproof · cited by 46
Cited by1
Results whose statement or proof uses this declaration.
- AddSubmonoid.addOrderOf_le_cardproof · cited by 0