Theorems · Theorem · commutative algebra
IsCoprime.dvd_of_dvd_mul_left
∀ {R : Type u} [inst : CommSemiring R] {x y z : R}, IsCoprime x y → x ∣ y * z → x ∣ z- Defined in
- Mathlib.RingTheory.Coprime.Basic
- Cited by
- 3 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
- one_mulproof · cited by 2,841
- mul_assocproof · cited by 1,667
- add_mulproof · cited by 363
- IsCoprimestatement and proof · cited by 321
- mul_right_commproof · cited by 108
- dvd_mul_leftproof · cited by 47
- dvd_addproof · cited by 25
- Dvd.dvd.mul_leftproof · cited by 14
Cited by3
Results whose statement or proof uses this declaration.
- PerfectField.separable_iff_squarefreeproof · cited by 2
- IsCoprime.wronskian_eq_zero_iffproof · cited by 1
- Polynomial.quo_mul_prod_add_sum_rem_mul_prod_uniqueproof · cited by 1