Theorems · Theorem · group theory
infinite_not_isOfFinAddOrder
∀ {G : Type u_1} [inst : AddLeftCancelMonoid G] {x : G}, ¬IsOfFinAddOrder x → {y | ¬IsOfFinAddOrder y}.Infinite- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddLeftCancelMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Set.ofPredstatement and proof · cited by 6,101
- Set.imageproof · cited by 5,609
- Set.Finiteproof · cited by 1,814
- Set.Ioiproof · cited by 1,463
- Set.InjOnproof · cited by 543
- mul_posproof · cited by 374
- Set.Infinitestatement and proof · cited by 263
- IsOfFinAddOrderstatement and proof · cited by 105
- AddLeftCancelMonoidstatement and proof · cited by 37
- Set.injOn_of_injectiveproof · cited by 28
- isOfFinAddOrder_iff_nsmul_eq_zeroproof · cited by 27
Cited by2
Results whose statement or proof uses this declaration.
- isOfFinAddOrder_of_finiteproof · cited by 10
- AddCircle.card_addOrderOf_eq_totientproof · cited by 0