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Theorems · Theorem · group theory

isOfFinAddOrder_neg_iff

∀ {G : Type u_1} [inst : AddGroup G] {x : G}, IsOfFinAddOrder (-x) ↔ IsOfFinAddOrder x

Inverses of elements of finite additive order have finite additive order.

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

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

IsOfFinAddOrder.of_neg · cited by 0IsOfFinAddOrder.of_negIsOfFinAddOrder.neg · cited by 0IsOfFinAddOrder.negAddGroup · cited by 4410AddGroupneg_eq_zero · cited by 171neg_eq_zeroIsOfFinAddOrder · cited by 105IsOfFinAddOrderisOfFinAddOrder_iff_nsmul_eq_zero · cited by 27isOfFinAddOrder_iff_nsmul…neg_nsmul · cited by 19neg_nsmulisOfFinAddOrder_neg_iffCITED BYCITES

Cites5

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Cited by2

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