Theorems · Inductive type · group theory
IsCancelMulZero
(M₀ : Type u) → [Mul M₀] → [Zero M₀] → Prop
A mixin for cancellative multiplication by nonzero elements.
- Defined in
- Mathlib.Algebra.GroupWithZero.Defs
- Cited by
- 177 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 3 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by210
Results whose statement or proof uses this declaration.
- Prime.irreduciblestatement and proof · cited by 54
- smul_eq_zerostatement and proof · cited by 40
- Function.Injective.isDomainproof · cited by 27
- smul_left_injectivestatement and proof · cited by 25
- smul_right_injectivestatement and proof · cited by 24
- dvd_antisymmstatement and proof · cited by 23
- IsAddTorsionFree.of_isTorsionFreestatement and proof · cited by 22
- smul_eq_zero_iff_rightstatement and proof · cited by 17
- irreducible_iff_primestatement and proof · cited by 15
- IsRegular.of_ne_zerostatement and proof · cited by 15
- IsLocalization.isDomain_of_le_nonZeroDivisorsproof · cited by 11
- smul_eq_zero_iff_leftstatement and proof · cited by 10
Showing the 200 most cited of 210.