Theorems · Theorem · commutative algebra
EuclideanDomain.zero_div
∀ {R : Type u} [inst : EuclideanDomain R] {a : R}, 0 / a = 0- Defined in
- Mathlib.Algebra.EuclideanDomain.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- EuclideanDomain
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- EuclideanDomainstatement and proof · cited by 124
- mul_div_cancel_right₀proof · cited by 70
- by_casesproof · cited by 31
- EuclideanDomain.div_zeroproof · cited by 17
Cited by5
Results whose statement or proof uses this declaration.
- RatFunc.num_divproof · cited by 6
- Module.reflection_mul_reflection_pow_applyproof · cited by 2
- EuclideanDomain.lcm_zero_leftproof · cited by 1
- EuclideanDomain.lcm_zero_rightproof · cited by 1
- EuclideanDomain.div_divproof · cited by 0