Theorems · Theorem · group theory
zsmul_right_inj
∀ {G : Type u_2} [inst : AddGroup G] [IsAddTorsionFree G] {n : ℤ} {a b : G}, n ≠ 0 → (n • a = n • b ↔ a = b)- Defined in
- Mathlib.Algebra.Group.Torsion
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroupIsAddTorsionFree
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- IsAddTorsionFreestatement and proof · cited by 155
- zsmul_right_injectiveproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- AddCommGroup.zsmul_modEq_zsmulproof · cited by 1
- IsAddTorsionFree.zsmul_eq_zero_iff_rightproof · cited by 1
- zsmul_eq_zsmul_iff'proof · cited by 0