Theorems · Theorem · group theory
inv_eq_zero
∀ {G₀ : Type u_2} [inst : GroupWithZero G₀] {a : G₀}, a⁻¹ = 0 ↔ a = 0- Defined in
- Mathlib.Algebra.GroupWithZero.Basic
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 18 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.
- GroupWithZerostatement and proof · cited by 691
- inv_zeroproof · cited by 184
- inv_eq_iff_eq_invproof · cited by 17
Cited by15
Results whose statement or proof uses this declaration.
- meromorphicOrderAt_invproof · cited by 5
- Polynomial.span_singleton_annIdealGeneratorproof · cited by 4
- Function.support_invproof · cited by 3
- tendsto_riemannZeta_sub_one_divproof · cited by 3
- AdjoinRoot.minpoly_rootproof · cited by 3
- irrational_div_ratCast_iffproof · cited by 2
- ValuationSubring.inv_mem_nonunits_iffproof · cited by 2
- spectralValue_X_powproof · cited by 2
- HurwitzZeta.differentiableAt_update_of_residueproof · cited by 2
- Complex.hasSum_arctan_auxproof · cited by 1
- Polynomial.splits_iff_comp_splits_of_natDegree_eq_oneproof · cited by 1
- conductor_mul_differentIdealproof · cited by 1