Theorems · Theorem · group theory
IsOfFinAddOrder.finite_multiples
∀ {G : Type u_1} [inst : AddMonoid G] {a : G}, IsOfFinAddOrder a → (↑(AddSubmonoid.multiples a)).Finite- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 79 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- SetLike.coestatement · cited by 8,199
- AddMonoidstatement and proof · cited by 2,864
- Set.Finitestatement and proof · cited by 1,814
- Finset.rangeproof · cited by 1,341
- AddSubmonoidstatement · cited by 1,178
- Finset.imageproof · cited by 910
- Finset.finite_toSetproof · cited by 210
- addOrderOfproof · cited by 208
- IsOfFinAddOrderstatement and proof · cited by 105
- AddSubmonoid.multiplesstatement · cited by 40
- IsOfFinAddOrder.multiples_eq_image_range_addOrderOfproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- AddRightCancelMonoid.finite_multiplesproof · cited by 1
- AddMonoid.finite_set_isOfFiniteOrder_of_descentproof · cited by 1
- finite_multiplesproof · cited by 1