Theorems · Theorem · commutative algebra
EuclideanDomain.div_mul
∀ {R : Type u} [inst : EuclideanDomain R] {x y z : R}, y ∣ x → y * z ∣ x → x / (y * z) = x / y / z- Defined in
- Mathlib.Algebra.EuclideanDomain.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 52 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_commproof · cited by 2,262
- MulZeroClass.mul_zeroproof · cited by 2,091
- eq_or_neproof · cited by 1,117
- EuclideanDomainstatement and proof · cited by 124
- EuclideanDomain.div_zeroproof · cited by 17
- EuclideanDomain.eq_div_of_mul_eq_rightproof · cited by 9
- EuclideanDomain.mul_div_assocproof · cited by 8
- EuclideanDomain.mul_div_mul_cancelproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- EuclideanDomain.div_divproof · cited by 0