Theorems · Theorem · commutative algebra
EuclideanDomain.div_dvd_of_dvd
∀ {R : Type u} [inst : EuclideanDomain R] {p q : R}, q ∣ p → p / q ∣ p- Defined in
- Mathlib.Algebra.EuclideanDomain.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 20 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_commproof · cited by 2,262
- EuclideanDomainstatement and proof · cited by 124
- mul_div_cancel_right₀proof · cited by 70
- dvd_zeroproof · cited by 63
- zero_dvd_iffproof · cited by 37
- EuclideanDomain.mul_div_assocproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- RatFunc.num_div_dvdproof · cited by 2
- RatFunc.denom_div_dvdproof · cited by 1