Theorems · Theorem · group theory
div_zero
∀ {G₀ : Type u_2} [inst : GroupWithZero G₀] (a : G₀), a / 0 = 0- Defined in
- Mathlib.Algebra.GroupWithZero.Basic
- Cited by
- 251 results in Mathlib
- Foundations
- Depth 12 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.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MulZeroClass.mul_zeroproof · cited by 2,091
- div_eq_mul_invproof · cited by 715
- GroupWithZerostatement and proof · cited by 691
- inv_zeroproof · cited by 184
Cited by251
Results whose statement or proof uses this declaration.
- Complex.arg_zeroproof · cited by 22
- MeasureTheory.tilted_zero_measureproof · cited by 12
- InnerProductGeometry.angle_add_eq_arccos_of_inner_eq_zeroproof · cited by 8
- Complex.Gamma_zeroproof · cited by 7
- EuclideanGeometry.inversion_selfproof · cited by 6
- RatFunc.num_divproof · cited by 6
- Nat.cast_div_charZeroproof · cited by 6
- IntervalIntegrable.comp_mul_leftproof · cited by 6
- AddCircle.scaled_exp_map_periodicproof · cited by 6
- Asymptotics.isEquivalent_of_tendsto_oneproof · cited by 5
- seminormFromBounded_bddAbove_rangeproof · cited by 5
- Rat.floor_intCast_div_natCastproof · cited by 5
Showing the 200 most cited of 251.