Theorems · Definition · group theory
finEquivZMultiples
{G : Type u_1} → [inst : AddGroup G] → {x : G} → IsOfFinAddOrder x → Fin (addOrderOf x) ≃ ↥(AddSubgroup.zmultiples x)The equivalence between Fin (addOrderOf a) and
Subgroup.zmultiples a, sending i to i • a.
- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 50 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.
- Equivstatement · cited by 8,337
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- AddSubgroup.zmultiplesstatement · cited by 493
- Equiv.transproof · cited by 337
- addOrderOfstatement · cited by 208
- IsOfFinAddOrderstatement and proof · cited by 105
- Equiv.setCongrproof · cited by 13
- finEquivMultiplesproof · cited by 7
- IsOfFinAddOrder.multiples_eq_zmultiplesproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- Fintype.card_zmultiplesproof · cited by 3
- finEquivZMultiples_symm_applystatement · cited by 1
- zmultiplesEquivZMultiplesproof · cited by 1
- nsmul_finEquivZMultiples_symm_applystatement and proof · cited by 0
- zmultiples_equiv_zmultiples_applyproof · cited by 0
- finEquivZMultiples_applystatement · cited by 0