Theorems · Theorem · group theory
IsLeftRegular.mul_left_eq_zero_iff
∀ {R : Type u_1} [inst : MulZeroClass R] {a b : R}, IsLeftRegular b → (b * a = 0 ↔ a = 0)- Defined in
- Mathlib.Algebra.GroupWithZero.Regular
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- MulZeroClass
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.
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClassstatement and proof · cited by 232
- IsLeftRegularstatement and proof · cited by 97
Cited by3
Results whose statement or proof uses this declaration.
- HahnSeries.order_single_mul_of_isRegularproof · cited by 1
- Polynomial.rootMultiplicity_scaleRootsproof · cited by 1
- IsLeftRegular.mem_nonZeroDivisorsLeftproof · cited by 1