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Theorems · Theorem · group theory

AddCommute.isOfFinAddOrder_add

∀ {G : Type u_1} [inst : AddMonoid G] {x y : G},
  AddCommute x y → IsOfFinAddOrder x → IsOfFinAddOrder y → IsOfFinAddOrder (x + y)

Commuting elements of finite additive order are closed under addition.

Defined in
Mathlib.GroupTheory.OrderOfElement
Cited by
1 results in Mathlib
Foundations
Depth 39 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.

IsOfFinAddOrder.add · cited by 0IsOfFinAddOrder.addAddMonoid · cited by 2864AddMonoidmul_pos · cited by 374mul_posAddCommute · cited by 185AddCommuteIsOfFinAddOrder · cited by 105IsOfFinAddOrderIsOfFinAddOrder.addOrderOf_pos · cited by 16IsOfFinAddOrder.addOrderO…addOrderOf_pos_iff · cited by 10addOrderOf_pos_iffAddCommute.addOrderOf_add_dvd_mul_addOrderOf · cited by 1AddCommute.addOrderOf_add…AddCommute.isOfFinAddOrder_addCITED BYCITES

Cites7

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Cited by1

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