Theorems · Theorem · group theory
IsOfFinAddOrder.addOrderOf_nsmul
∀ {G : Type u_1} [inst : AddMonoid G] (x : G) (n : ℕ),
IsOfFinAddOrder x → addOrderOf (n • x) = addOrderOf x / (addOrderOf x).gcd n- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 36 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.
Cites6
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
- addOrderOfstatement · cited by 208
- IsOfFinAddOrderstatement and proof · cited by 105
- Function.minimalPeriodproof · cited by 100
- add_left_iterateproof · cited by 10
- Function.minimalPeriod_iterate_eq_div_gcd'proof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- AddCircle.gcd_mul_addOrderOf_div_eqproof · cited by 3
- addOrderOf_nsmulproof · cited by 2
- Nat.Coprime.addOrderOf_nsmulproof · cited by 1