Theorems · Theorem · commutative algebra
IsCoprime.mul_left
∀ {R : Type u} [inst : CommSemiring R] {x y z : R}, IsCoprime x z → IsCoprime y z → IsCoprime (x * y) z- Defined in
- Mathlib.RingTheory.Coprime.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- IsCoprimestatement and proof · cited by 321
Cited by6
Results whose statement or proof uses this declaration.
- IsCoprime.prod_leftproof · cited by 3
- IsCoprime.mul_left_iffproof · cited by 2
- IsCoprime.mul_rightproof · cited by 2
- Int.isCoprime_of_sq_sumproof · cited by 1
- Polynomial.Separable.mulproof · cited by 1
- Polynomial.abcproof · cited by 0