Theorems · Theorem · commutative algebra
isCoprime_of_prime_dvd
∀ {R : Type u} [inst : CommRing R] [IsDomain R] [IsPrincipalIdealRing R] {x y : R},
¬(x = 0 ∧ y = 0) → (∀ (z : R), Prime z → z ∣ x → ¬z ∣ y) → IsCoprime x y- Defined in
- Mathlib.RingTheory.PrincipalIdealDomain
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- IsDomainstatement and proof · cited by 2,196
- Irreducibleproof · cited by 496
- IsCoprimestatement · cited by 321
- Primestatement and proof · cited by 277
- IsPrincipalIdealRingstatement and proof · cited by 131
- Irreducible.primeproof · cited by 4
- isCoprime_of_irreducible_dvdproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- isCoprime_of_gcd_eq_one_of_FLTproof · cited by 0