Theorems · Theorem · group theory
nsmul_eq_zero_iff_modEq
∀ {G : Type u_1} [inst : AddMonoid G] {x : G} {n : ℕ}, n • x = 0 ↔ n ≡ 0 [MOD addOrderOf x]- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 33 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.
Cites5
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.ModEqstatement · cited by 225
- addOrderOfstatement · cited by 208
- addOrderOf_dvd_iff_nsmul_eq_zeroproof · cited by 17
- Nat.modEq_zero_iff_dvdproof · cited by 17
Cited by3
Results whose statement or proof uses this declaration.
- nsmul_eq_nsmul_iff_modEqproof · cited by 4
- AddRightCancelMonoid.nsmul_eq_nsmul_iff_modEqproof · cited by 3
- IsOfFinAddOrder.nsmul_eq_nsmul_iff_modEqproof · cited by 1