Theorems · Theorem · commutative algebra
Associates.mem_factors_iff_dvd
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : UniqueFactorizationMonoid α] {a p : α},
a ≠ 0 → Irreducible p → (Associates.mk p ∈ (Associates.mk a).factors ↔ p ∣ a)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidWithZerostatement and proof · cited by 913
- Irreduciblestatement and proof · cited by 496
- UniqueFactorizationMonoidstatement and proof · cited by 279
- Associatesstatement · cited by 210
- Associates.mkstatement and proof · cited by 137
- Associates.factorsstatement and proof · cited by 97
- Associates.FactorSetstatement · cited by 52
- Associates.mk_dvd_mkproof · cited by 9
- Associates.dvd_of_mem_factorsproof · cited by 2
- Associates.mem_factors_of_dvdproof · cited by 1
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