Theorems · Theorem · group theory
AddRightCancelMonoid.infinite_multiples
∀ {G : Type u_1} [inst : AddRightCancelMonoid G] {a : G}, (↑(AddSubmonoid.multiples a)).Infinite ↔ ¬IsOfFinAddOrder a- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddRightCancelMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coestatement · cited by 8,199
- AddSubmonoidstatement · cited by 1,178
- Iff.notproof · cited by 489
- Set.Infinitestatement · cited by 263
- IsOfFinAddOrderstatement · cited by 105
- AddSubmonoid.multiplesstatement · cited by 40
- AddRightCancelMonoidstatement and proof · cited by 25
- AddRightCancelMonoid.finite_multiplesproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- AddRightCancelMonoid.Nat.card_addSubmonoidMultiplesproof · cited by 0