Theorems · Theorem · commutative algebra

Ideal.count_le_of_ideal_ge

∀ {T : Type u_4} [inst : CommRing T] [inst_1 : IsDedekindDomain T] {I J : Ideal T},
  I ≤ J →
    I ≠ ⊥ →
      ∀ (K : Ideal T),
        Multiset.count K (UniqueFactorizationMonoid.normalizedFactors J) ≤
          Multiset.count K (UniqueFactorizationMonoid.normalizedFactors I)

Defined in: Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas
Cited by: 3 results in Mathlib
Foundations: Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing IsDedekindDomain

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Cites10

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
Idealstatement and proof · cited by 4,748
Bot.botstatement and proof · cited by 4,720
IsDedekindDomainstatement and proof · cited by 668
Multiset.countstatement · cited by 302
UniqueFactorizationMonoid.normalizedFactorsstatement · cited by 151
Ideal.dvd_iff_leproof · cited by 33
ne_bot_of_le_ne_botproof · cited by 18
Multiset.le_iff_countproof · cited by 14
UniqueFactorizationMonoid.dvd_iff_normalizedFactors_le_normalizedFactorsproof · cited by 11

Cited by3

Results whose statement or proof uses this declaration.

Ideal.sup_eq_prod_inf_factorsproof · cited by 3
count_le_of_ideal_geproof · cited by 0
IsDedekindDomain.HeightOneSpectrum.multiplicity_le_of_ideal_geproof · cited by 0