Theorems · Theorem · commutative algebra
EuclideanDomain.div_zero
∀ {R : Type u} [inst : EuclideanDomain R] (a : R), a / 0 = 0- Defined in
- Mathlib.Algebra.EuclideanDomain.Defs
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
- Assumes
- EuclideanDomain
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.
- EuclideanDomainstatement and proof · cited by 124
- EuclideanDomain.quotient_zeroproof · cited by 1
Cited by17
Results whose statement or proof uses this declaration.
- EuclideanDomain.mul_div_assocproof · cited by 8
- EuclideanDomain.zero_divproof · cited by 5
- PythagoreanTriple.normalizeproof · cited by 2
- EuclideanDomain.lcm_dvdproof · cited by 1
- Polynomial.div_C_mulproof · cited by 1
- ArithmeticFunction.vonMangoldt.not_summable_residueClass_prime_divproof · cited by 1
- EuclideanDomain.mul_div_mul_cancelproof · cited by 1
- EuclideanDomain.div_mulproof · cited by 1
- EuclideanDomain.dvd_lcm_leftproof · cited by 1
- EuclideanDomain.dvd_lcm_rightproof · cited by 1
- Polynomial.leadingCoeff_divproof · cited by 0
- EuclideanDomain.div_divproof · cited by 0