Theorems · Theorem · commutative algebra
WfDvdMonoid.isRelPrime_of_no_irreducible_factors
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [WfDvdMonoid α] {x y : α},
¬(x = 0 ∧ y = 0) → (∀ (z : α), Irreducible z → z ∣ x → ¬z ∣ y) → IsRelPrime x y- Cited by
- 2 results in Mathlib
- Foundations
- Depth 16 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.
- IsUnitproof · cited by 1,602
- CommMonoidWithZerostatement and proof · cited by 913
- Irreduciblestatement and proof · cited by 496
- Dvd.dvd.transproof · cited by 148
- IsRelPrimestatement · cited by 136
- WfDvdMonoidstatement and proof · cited by 37
- WfDvdMonoid.exists_irreducible_factorproof · cited by 12
- isRelPrime_of_no_nonunits_factorsproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- isCoprime_of_irreducible_dvdproof · cited by 3
- UniqueFactorizationMonoid.isRelPrime_iff_no_prime_factorsproof · cited by 2