Theorems · Theorem · group theory
smul_ne_zero_iff_ne
∀ {α : Type u_10} {β : Type u_11} [inst : Group α] [inst_1 : AddMonoid β] [inst_2 : DistribMulAction α β] (a : α)
{x : β}, a • x ≠ 0 ↔ x ≠ 0- Cited by
- 11 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
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.
- Groupstatement and proof · cited by 6,238
- AddMonoidstatement and proof · cited by 2,864
- DistribMulActionstatement and proof · cited by 584
- smul_eq_zero_iff_eqproof · cited by 4
Cited by11
Results whose statement or proof uses this declaration.
- smul_rayOfNeZerostatement · cited by 3
- Module.Basis.map_orientation_eq_det_inv_smulproof · cited by 3
- units_smul_eq_self_iffproof · cited by 3
- OnePoint.smul_some_eq_iteproof · cited by 2
- Module.Ray.neg_units_smulproof · cited by 2
- Module.Ray.units_smul_of_posproof · cited by 2
- Projectivization.SL_mulAction_kerproof · cited by 1
- Module.Basis.orientation_unitsSMulproof · cited by 1
- OnePoint.smul_infty_defproof · cited by 1
- Projectivization.smul_mkstatement · cited by 0
- Projectivization.PGL.mk_smul_mkstatement · cited by 0