Theorems · Theorem · group theory
Units.mul_left_eq_zero
∀ {M₀ : Type u_2} [inst : MonoidWithZero M₀] (u : M₀ˣ) {a : M₀}, a * ↑u = 0 ↔ a = 0- Cited by
- 2 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- MonoidWithZero
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.
- Unitsstatement and proof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- MonoidWithZerostatement and proof · cited by 456
- Units.mul_inv_cancel_rightproof · cited by 20
- mul_eq_zero_of_leftproof · cited by 13
Cited by2
Results whose statement or proof uses this declaration.
- IsUnit.mul_left_eq_zeroproof · cited by 10
- ZMod.add_self_eq_zero_iff_eq_zeroproof · cited by 2