Theorems · Theorem · commutative algebra

Associates.exists_prime_dvd_of_not_inf_one

∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : UniqueFactorizationMonoid α] {a b : α},
  a ≠ 0 → b ≠ 0 → Associates.mk a ⊓ Associates.mk b ≠ 1 → ∃ p, Prime p ∧ p ∣ a ∧ p ∣ b

Defined in

Mathlib.RingTheory.UniqueFactorizationDomain.FactorSet

Cited by

1 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidWithZeroUniqueFactorizationMonoid