Theorems · Theorem · group theory
smul_eq_zero_iff_eq
∀ {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
- 4 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
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.
- Groupstatement and proof · cited by 6,238
- AddMonoidstatement and proof · cited by 2,864
- smul_zeroproof · cited by 665
- DistribMulActionstatement and proof · cited by 584
- inv_smul_smulproof · cited by 76
Cited by4
Results whose statement or proof uses this declaration.
- smul_ne_zero_iff_neproof · cited by 11
- IsUnit.smul_eq_zeroproof · cited by 2
- LinearMap.BilinForm.IsRefl.groupSMulproof · cited by 0
- Polynomial.isUnit_leadingCoeff_mul_right_eq_zero_iffproof · cited by 0