Theorems · Theorem · group theory
nsmul_eq_zero_iff
∀ {M : Type u_1} [inst : AddMonoid M] [IsAddTorsionFree M] {n : ℕ} {a : M}, n • a = 0 ↔ a = 0 ∨ n = 0- Defined in
- Mathlib.Algebra.Group.Torsion
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoidIsAddTorsionFree
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
- eq_or_neproof · cited by 1,117
- IsAddTorsionFreestatement and proof · cited by 155
- zero_nsmulproof · cited by 137
- nsmul_eq_zero_iff_rightproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- not_isOfFinAddOrder_of_isAddTorsionFreeproof · cited by 7
- nsmul_eq_zero_iff_leftproof · cited by 1