Theorems · Theorem · commutative algebra
EuclideanDomain.eq_div_of_mul_eq_right
∀ {R : Type u} [inst : EuclideanDomain R] {a b c : R}, a ≠ 0 → a * b = c → b = c / a- Defined in
- Mathlib.Algebra.EuclideanDomain.Basic
- Cited by
- 9 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.
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
- mul_div_cancel_left₀proof · cited by 111
Cited by9
Results whose statement or proof uses this declaration.
- EuclideanDomain.mul_add_div_leftproof · cited by 1
- EuclideanDomain.sub_mul_div_leftproof · cited by 1
- EuclideanDomain.mul_div_mul_cancelproof · cited by 1
- EuclideanDomain.div_mulproof · cited by 1
- EuclideanDomain.mul_sub_div_leftproof · cited by 1
- EuclideanDomain.dvd_lcm_rightproof · cited by 1
- EuclideanDomain.add_mul_div_leftproof · cited by 1
- EuclideanDomain.div_add_div_of_dvdproof · cited by 0
- EuclideanDomain.div_sub_div_of_dvdproof · cited by 0