Theorems · Theorem · group theory
isPeriodicPt_add_iff_nsmul_eq_zero
∀ {G : Type u_1} [inst : AddMonoid G] {n : ℕ} (x : G), Function.IsPeriodicPt (fun x_1 => x + x_1) n 0 ↔ n • x = 0- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, 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
- Nat.iterateproof · cited by 740
- Function.IsPeriodicPtstatement · cited by 68
- add_left_iterate_apply_zeroproof · cited by 3
Cited by10
Results whose statement or proof uses this declaration.
- isOfFinAddOrder_iff_nsmul_eq_zeroproof · cited by 27
- addOrderOf_dvd_of_nsmul_eq_zeroproof · cited by 6
- addOrderOf_eq_addOrderOf_iffproof · cited by 3
- addOrderOf_eq_iffproof · cited by 2
- addOrderOf_le_of_nsmul_eq_zeroproof · cited by 2
- nsmul_ne_zero_of_lt_addOrderOfproof · cited by 1
- AddCommMonoid.addTorsion.isAddTorsionproof · cited by 1
- addOrderOf_eq_prime_iffproof · cited by 1
- addOrderOf_eq_prime_powproof · cited by 1
- exists_zsmul_eq_zeroproof · cited by 0