Theorems · Theorem · group theory
Fintype.card_zmultiples
∀ {G : Type u_1} [inst : AddGroup G] [inst_1 : Fintype G] {x : G},
Fintype.card ↥(AddSubgroup.zmultiples x) = addOrderOf xSee also Nat.card_zmultiples.
- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Fintypestatement and proof · cited by 7,736
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- Fintype.cardstatement · cited by 1,386
- AddSubgroup.zmultiplesstatement · cited by 493
- Fintype.card_finproof · cited by 270
- addOrderOfstatement and proof · cited by 208
- Fintype.card_eqproof · cited by 19
- isOfFinAddOrder_of_finiteproof · cited by 10
- finEquivZMultiplesproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- addOrderOf_dvd_cardproof · cited by 5
- IsAddCyclic.card_nsmul_eq_zero_leproof · cited by 1
- card_zmultiples_leproof · cited by 0