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Theorems · Theorem · group theory

addOrderOf_eq_zero

∀ {G : Type u_1} [inst : AddMonoid G] {x : G}, ¬IsOfFinAddOrder x → addOrderOf x = 0
Defined in
Mathlib.GroupTheory.OrderOfElement
Cited by
5 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddMonoid
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Around this declaration

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

addOrderOf_eq_zero_iff · cited by 9addOrderOf_eq_zero_iffzsmul_smul_addOrderOf · cited by 2zsmul_smul_addOrderOfNat.card_addSubmonoidMultiples · cited by 1Nat.card_addSubmonoidMult…Nat.Coprime.addOrderOf_nsmul · cited by 1Coprime.addOrderOf_nsmulAddRightCancelMonoid.Nat.card_addSubmonoidMultiples · cited by 0Nat.card_addSubmonoidMult…AddMonoid · cited by 2864AddMonoidaddOrderOf · cited by 208addOrderOfIsOfFinAddOrder · cited by 105IsOfFinAddOrderaddOrderOf_eq_zeroCITED BYCITES

Cites3

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Cited by5

Results whose statement or proof uses this declaration.