Theorems · Theorem · group theory
addOrderOf_dvd_natCard
∀ {G : Type u_6} [inst : AddGroup G] (x : G), addOrderOf x ∣ Nat.card G- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypeproof · cited by 7,736
- AddGroupstatement and proof · cited by 4,410
- Nat.cardstatement · cited by 844
- Infiniteproof · cited by 352
- addOrderOfstatement and proof · cited by 208
- Nat.card_eq_fintype_cardproof · cited by 200
- dvd_zeroproof · cited by 63
- Nat.card_eq_zero_of_infiniteproof · cited by 46
- fintypeOrInfiniteproof · cited by 14
- addOrderOf_dvd_cardproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- card_nsmul_eq_zero'proof · cited by 3
- AddGroup.exponent_dvd_nat_cardproof · cited by 2
- AddSubgroup.addOrderOf_dvd_natCardproof · cited by 1
- mod_natCard_nsmulproof · cited by 1
- not_isAddCyclic_iff_exponent_eq_primeproof · cited by 0
- mod_natCard_zsmulproof · cited by 0