Theorems · Theorem · group theory
isUnit_iff_ne_zero
∀ {G₀ : Type u_3} [inst : GroupWithZero G₀] {a : G₀}, IsUnit a ↔ a ≠ 0- Cited by
- 30 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupWithZero
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.
- IsUnitstatement · cited by 1,602
- GroupWithZerostatement and proof · cited by 691
- Units.exists_iff_ne_zeroproof · cited by 2
Cited by30
Results whose statement or proof uses this declaration.
- Ne.isUnitproof · cited by 99
- map_ne_zeroproof · cited by 20
- IsIntegralClosure.isLocalizationproof · cited by 13
- Polynomial.not_irreducible_Cproof · cited by 5
- Algebra.FormallyUnramified.of_isSeparableproof · cited by 5
- Polynomial.associated_of_dvd_of_natDegree_leproof · cited by 4
- FiniteDimensional.of_totallyBounded_nhds_zeroproof · cited by 3
- MeasureTheory.Measure.integral_comp_smulproof · cited by 3
- Valuation.exists_pow_Uniformizerproof · cited by 3
- MeasureTheory.integrable_comp_smul_iffproof · cited by 2
- Polynomial.monic_normalizeproof · cited by 2
- IsLocalization.AtPrime.not_isFieldproof · cited by 2