Theorems · Theorem · commutative algebra
IsCoprime.dvd_of_dvd_mul_right
∀ {R : Type u} [inst : CommSemiring R] {x y z : R}, IsCoprime x z → x ∣ y * z → x ∣ y- Defined in
- Mathlib.RingTheory.Coprime.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- mul_oneproof · cited by 3,885
- mul_assocproof · cited by 1,667
- mul_addproof · cited by 413
- IsCoprimestatement and proof · cited by 321
- mul_left_commproof · cited by 184
- dvd_mul_leftproof · cited by 47
- dvd_addproof · cited by 25
- Dvd.dvd.mul_leftproof · cited by 14
Cited by4
Results whose statement or proof uses this declaration.
- Complex.isPrimitiveRoot_exp_of_isCoprimeproof · cited by 2
- IsCoprime.wronskian_eq_zero_iffproof · cited by 1
- Polynomial.quo_mul_prod_add_sum_rem_mul_prod_uniqueproof · cited by 1
- IsDedekindDomain.map_differentIdeal_dvd_differentIdealproof · cited by 1