Theorems · Theorem · group theory
IsAddTorsionFree.zsmul_eq_zero_iff
∀ {G : Type u_2} [inst : AddGroup G] [IsAddTorsionFree G] {n : ℤ} {a : G}, n • a = 0 ↔ a = 0 ∨ n = 0- Defined in
- Mathlib.Algebra.Group.Torsion
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroupIsAddTorsionFree
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.
- AddGroupstatement and proof · cited by 4,410
- eq_or_neproof · cited by 1,117
- IsAddTorsionFreestatement and proof · cited by 155
- zero_nsmulproof · cited by 137
- ofNat_zsmulproof · cited by 24
- IsAddTorsionFree.zsmul_eq_zero_iff_rightproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IsAddTorsionFree.zsmul_eq_zero_iff_leftproof · cited by 1