Theorems · Theorem · group theory
zero_div
∀ {G₀ : Type u_2} [inst : GroupWithZero G₀] (a : G₀), 0 / a = 0- Defined in
- Mathlib.Algebra.GroupWithZero.Basic
- Cited by
- 222 results in Mathlib
- Foundations
- Depth 11 from the axioms, rests on 101 definitions · uses no axioms
- 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.
- MulZeroClass.zero_mulproof · cited by 1,625
- div_eq_mul_invproof · cited by 715
- GroupWithZerostatement and proof · cited by 691
Cited by222
Results whose statement or proof uses this declaration.
- Complex.ofReal_invproof · cited by 62
- Complex.exp_zeroproof · cited by 43
- Complex.arg_ofReal_of_nonnegproof · cited by 16
- InnerProductGeometry.angle_zero_leftproof · cited by 14
- InnerProductGeometry.angle_zero_rightproof · cited by 10
- InnerProductGeometry.angle_add_eq_arccos_of_inner_eq_zeroproof · cited by 8
- Complex.sin_zeroproof · cited by 8
- Real.logb_oneproof · cited by 7
- InnerProductSpace.gramSchmidt_orthogonalproof · cited by 6
- ProbabilityTheory.integral_id_gaussianRealproof · cited by 6
- Real.rpowIntegrand₀₁_eq_pow_divproof · cited by 6
- ExistsContDiffBumpBase.u_existsproof · cited by 5
Showing the 200 most cited of 222.