Theorems · Definition · group theory
IsOfFinAddOrder.addUnit
{M : Type u_6} → [inst : AddMonoid M] → {x : M} → IsOfFinAddOrder x → AddUnits MIf the additive order of x is finite, then x is an additive
unit with inverse (addOrderOf x - 1) • x.
- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 23 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.
Cites4
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
- AddUnitsstatement · cited by 325
- addOrderOfproof · cited by 208
- IsOfFinAddOrderstatement and proof · cited by 105
Cited by3
Results whose statement or proof uses this declaration.
- IsOfFinAddOrder.isAddUnitproof · cited by 1
- IsOfFinAddOrder.val_neg_addUnitstatement and proof · cited by 0
- IsOfFinAddOrder.val_addUnitstatement and proof · cited by 0