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Theorems · Theorem · group theory

IsOfFinAddOrder.exists_nsmul_eq_zero

∀ {G : Type u_1} [inst : AddMonoid G] {x : G}, IsOfFinAddOrder x → ∃ n, 0 < n ∧ n • x = 0

Alias of the forward direction of isOfFinAddOrder_iff_nsmul_eq_zero.

Defined in
Mathlib.GroupTheory.OrderOfElement
Cited by
6 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext, Quot.sound
Assumes
AddMonoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsAddTorsion.extension_closed · cited by 2IsAddTorsion.extension_cl…IsAddTorsion.module_of_torsion · cited by 2IsAddTorsion.module_of_to…AddMonoidHom.isOfFinAddOrder · cited by 2AddMonoidHom.isOfFinAddOr…isAddTorsion_iff_isTorsion_int · cited by 2isAddTorsion_iff_isTorsio…isAddTorsion_iff_isTorsion_nat · cited by 1isAddTorsion_iff_isTorsio…IsOfFinAddOrder.addGroupMultiples · cited by 0IsOfFinAddOrder.addGroupM…IsOfFinAddOrder.apply · cited by 0IsOfFinAddOrder.applyAddMonoid · cited by 2864AddMonoidIsOfFinAddOrder · cited by 105IsOfFinAddOrderisOfFinAddOrder_iff_nsmul_eq_zero · cited by 27isOfFinAddOrder_iff_nsmul…IsOfFinAddOrder.exists_nsmul_…CITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by7

Results whose statement or proof uses this declaration.