Theorems · Theorem · group theory
IsOfFinAddOrder.zsmul
∀ {G : Type u_1} [inst : AddGroup G] {x : G}, IsOfFinAddOrder x → ∀ {i : ℤ}, IsOfFinAddOrder (i • x)- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- addOrderOfproof · cited by 208
- IsOfFinAddOrderstatement and proof · cited by 105
- isOfFinAddOrder_iff_nsmul_eq_zeroproof · cited by 27
- IsOfFinAddOrder.addOrderOf_posproof · cited by 16
- zsmul_smul_addOrderOfproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- IsOfFinAddOrder.of_mem_zmultiplesproof · cited by 1