Theorems · Theorem · group theory
zsmul_smul_addOrderOf
∀ {G : Type u_1} [inst : AddGroup G] {x : G} {i : ℤ}, addOrderOf x • i • x = 0- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 37 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.
Cites10
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
- mul_commproof · cited by 2,262
- addOrderOfstatement and proof · cited by 208
- zero_nsmulproof · cited by 137
- natCast_zsmulproof · cited by 118
- IsOfFinAddOrderproof · cited by 105
- mul_zsmul'proof · cited by 16
- zsmul_zeroproof · cited by 14
- addOrderOf_nsmul_eq_zeroproof · cited by 11
- addOrderOf_eq_zeroproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- IsOfFinAddOrder.zsmulproof · cited by 1
- addOrderOf_dvd_of_mem_zmultiplesproof · cited by 1