Theorems · Theorem · commutative algebra
EuclideanDomain.mul_div_mul_cancel
∀ {R : Type u} [inst : EuclideanDomain R] {a b c : R}, a ≠ 0 → c ∣ b → a * b / (a * c) = b / c- Defined in
- Mathlib.Algebra.EuclideanDomain.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 51 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MulZeroClass.mul_zeroproof · cited by 2,091
- mul_assocproof · cited by 1,667
- mul_ne_zeroproof · cited by 178
- EuclideanDomainstatement and proof · cited by 124
- mul_div_cancel_left₀proof · cited by 111
- mul_left_cancel₀proof · cited by 47
- mul_dvd_mul_leftproof · cited by 34
- EuclideanDomain.div_zeroproof · cited by 17
- EuclideanDomain.eq_div_of_mul_eq_rightproof · cited by 9
- EuclideanDomain.mul_div_assocproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- EuclideanDomain.div_mulproof · cited by 1