Theorems · Definition · group theory
finEquivMultiples
{G : Type u_1} → [inst : AddMonoid G] → {x : G} → IsOfFinAddOrder x → Fin (addOrderOf x) ≃ ↥(AddSubmonoid.multiples x)The equivalence between Fin (addOrderOf a) and
AddSubmonoid.multiples a, sending i to i • a
- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivstatement · cited by 8,337
- AddMonoidstatement and proof · cited by 2,864
- AddSubmonoidstatement · cited by 1,178
- addOrderOfstatement and proof · cited by 208
- IsOfFinAddOrderstatement and proof · cited by 105
- Equiv.ofBijectiveproof · cited by 70
- AddSubmonoid.multiplesstatement · cited by 40
Cited by9
Results whose statement or proof uses this declaration.
- finEquivZMultiplesproof · cited by 5
- finEquivMultiples_symm_applystatement and proof · cited by 2
- finEquivZMultiples_symm_applyproof · cited by 1
- Nat.card_addSubmonoidMultiplesproof · cited by 1
- multiplesEquivMultiplesproof · cited by 1
- finEquivMultiples_applystatement · cited by 1
- addOrderOf_eq_card_multiplesproof · cited by 0
- multiplesEquivMultiples_applyproof · cited by 0
- AddRightCancelMonoid.Nat.card_addSubmonoidMultiplesproof · cited by 0