Theorems · Theorem · commutative algebra
Associates.count_self
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : UniqueFactorizationMonoid α]
[inst_2 : DecidableEq (Associates α)] [inst_3 : (p : Associates α) → Decidable (Irreducible p)] [Nontrivial α]
{p : Associates α}, Irreducible p → p.count p.factors = 1- Cited by
- 4 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Multisetproof · cited by 2,627
- Nontrivialstatement and proof · cited by 2,416
- WithTop.someproof · cited by 1,128
- CommMonoidWithZerostatement and proof · cited by 913
- Irreduciblestatement and proof · cited by 496
- UniqueFactorizationMonoidstatement and proof · cited by 279
- Associatesstatement and proof · cited by 210
- Associates.factorsstatement and proof · cited by 97
- Associates.countstatement · cited by 79
- Associates.count.congr_simpproof · cited by 10
- Multiset.count_eq_one_of_memproof · cited by 8
- Associates.count_someproof · cited by 8
Cited by4
Results whose statement or proof uses this declaration.
- IsDedekindDomain.HeightOneSpectrum.intValuation_singletonproof · cited by 3
- FractionalIdeal.count_selfproof · cited by 3
- Associates.eq_pow_count_factors_of_dvd_powproof · cited by 2
- Associates.count_factors_eq_find_of_dvd_powproof · cited by 1