Theorems · Theorem · group theory
div_eq_zero_iff
∀ {G₀ : Type u_3} [inst : GroupWithZero G₀] {a b : G₀}, a / b = 0 ↔ a = 0 ∨ b = 0- Cited by
- 9 results in Mathlib
- Foundations
- Depth 20 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.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- div_eq_mul_invproof · cited by 715
- GroupWithZerostatement and proof · cited by 691
Cited by9
Results whose statement or proof uses this declaration.
- div_ne_zero_iffproof · cited by 7
- Complex.tan_eq_zero_iffproof · cited by 4
- NumberField.Units.dirichletUnitTheorem.seq_nextproof · cited by 3
- WittVector.RecursionBase.solution_nonzeroproof · cited by 1
- commProb_eq_zero_of_infiniteproof · cited by 1
- EuclideanGeometry.Sphere.secondInter_eq_self_iffproof · cited by 1
- Matrix.isParabolic_iff_existsproof · cited by 1
- FractionalIdeal.absNorm_eq_zero_iffproof · cited by 0