Theorems · Theorem · group theory
addOrderOf_eq_zero_iff
∀ {G : Type u_1} [inst : AddMonoid G] {x : G}, addOrderOf x = 0 ↔ ¬IsOfFinAddOrder x- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 22 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddMonoidstatement and proof · cited by 2,864
- LT.lt.ne'proof · cited by 1,417
- addOrderOfstatement and proof · cited by 208
- IsOfFinAddOrderstatement and proof · cited by 105
- IsOfFinAddOrder.addOrderOf_posproof · cited by 16
- addOrderOf_eq_zeroproof · cited by 5
Cited by9
Results whose statement or proof uses this declaration.
- addOrderOf_pos_iffproof · cited by 10
- AddMonoid.ExponentExists.of_finiteproof · cited by 2
- injective_zsmul_iff_not_isOfFinAddOrderproof · cited by 2
- AddRightCancelMonoid.injective_nsmul_iff_not_isOfFinAddOrderproof · cited by 1
- injective_nsmul_iff_not_isOfFinAddOrderproof · cited by 1
- addOrderOf_ne_zero_iffproof · cited by 1
- IsAddTorsionFree.addOrderOf_nonposproof · cited by 0
- addOrderOf_eq_zero_iff'proof · cited by 0
- IsOfFinAddOrder.piproof · cited by 0