Theorems · Theorem · group theory
inv_zero
∀ {G₀ : Type u} [inst : GroupWithZero G₀], 0⁻¹ = 0- Defined in
- Mathlib.Algebra.GroupWithZero.Defs
- Cited by
- 184 results in Mathlib
- Foundations
- Depth 11 from the axioms, rests on 94 definitions · uses no axioms
- Assumes
- GroupWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- GroupWithZerostatement and proof · cited by 691
- GroupWithZero.inv_zeroproof · cited by 3
Cited by184
Results whose statement or proof uses this declaration.
- div_zeroproof · cited by 251
- map_inv₀proof · cited by 106
- Real.rpow_negproof · cited by 36
- Real.log_invproof · cited by 35
- zero_zpowproof · cited by 19
- Complex.cpow_negproof · cited by 17
- inv_eq_zeroproof · cited by 15
- MeromorphicAt.invproof · cited by 9
- map_inv_natCast_smulproof · cited by 8
- RatFunc.num_divproof · cited by 6
- LieAlgebra.IsKilling.coroot_eq_zero_iffproof · cited by 6
- Polynomial.irreducible_mul_leadingCoeff_invproof · cited by 6