Theorems · Theorem · commutative algebra
IsCoprime.of_isCoprime_of_dvd_left
∀ {R : Type u} [inst : CommSemiring R] {x y z : R}, IsCoprime y z → x ∣ y → IsCoprime x z- Defined in
- Mathlib.RingTheory.Coprime.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses no axioms
- 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
- IsCoprimestatement and proof · cited by 321
- IsCoprime.of_mul_left_leftproof · cited by 8
Cited by4
Results whose statement or proof uses this declaration.
- IsCoprime.isUnit_of_dvd'proof · cited by 4
- Rat.isCoprime_num_denproof · cited by 2
- IsCoprime.of_isCoprime_of_dvd_rightproof · cited by 1
- IsCoprime.monoproof · cited by 0