Theorems · Theorem · commutative algebra
IsCoprime.of_mul_left_left
∀ {R : Type u} [inst : CommSemiring R] {x y z : R}, IsCoprime (x * y) z → IsCoprime x z- Defined in
- Mathlib.RingTheory.Coprime.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses no axioms
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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_assocproof · cited by 1,667
- IsCoprimestatement and proof · cited by 321
- mul_right_commproof · cited by 108
Cited by8
Results whose statement or proof uses this declaration.
- Polynomial.Separable.of_mul_leftproof · cited by 4
- IsCoprime.of_isCoprime_of_dvd_leftproof · cited by 4
- IsCoprime.of_mul_right_leftproof · cited by 4
- IsCoprime.of_mul_left_rightproof · cited by 3
- Polynomial.isUnit_of_self_mul_dvd_separableproof · cited by 2
- IsCoprime.mul_left_iffproof · cited by 2
- Polynomial.Separable.isCoprimeproof · cited by 1
- Fermat42.not_minimalproof · cited by 1