Theorems · Theorem · group theory
natAbs_nsmul_eq_zero
∀ {G : Type u_3} [inst : AddGroup G] {a : G} {n : ℤ}, n.natAbs • a = 0 ↔ n • a = 0- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext
- Assumes
- AddGroup
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.
- AddGroupstatement and proof · cited by 4,410
- neg_eq_zeroproof · cited by 171
- natCast_zsmulproof · cited by 118
- negSucc_zsmulproof · cited by 45
Cited by3
Results whose statement or proof uses this declaration.
- isAddTorsion_iff_isTorsion_intproof · cited by 2
- AddGroup.exponent_dvd_iff_forall_zsmul_eq_zeroproof · cited by 1
- abs_zsmul_eq_zeroproof · cited by 0