Theorems · Theorem · combinatorics
Multiset.le_iff_count
∀ {α : Type u_1} [inst : DecidableEq α] {s t : Multiset α}, s ≤ t ↔ ∀ (a : α), Multiset.count a s ≤ Multiset.count a t- Defined in
- Mathlib.Data.Multiset.Count
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Multisetstatement and proof · cited by 2,627
- Multiset.countstatement · cited by 302
- Multiset.coe_countproof · cited by 23
Cited by14
Results whose statement or proof uses this declaration.
- Ideal.sup_eq_prod_inf_factorsproof · cited by 3
- Ideal.count_le_of_ideal_geproof · cited by 3
- Polynomial.map_roots_leproof · cited by 3
- Multiset.le_card_smul_iff_subsetproof · cited by 2
- Polynomial.roots_expand_pow_map_iterateFrobenius_leproof · cited by 2
- IsDedekindDomain.HeightOneSpectrum.mem_integers_of_valuation_le_oneproof · cited by 1
- UniqueFactorizationMonoid.dvd_iff_emultiplicity_leproof · cited by 1
- Multiset.toEnumFinset_monoproof · cited by 1
- Multiset.le_bindproof · cited by 0
- Multiset.map_le_map_iffproof · cited by 0
- Polynomial.isRoot_of_isRoot_iff_dvd_derivative_mulproof · cited by 0
- Polynomial.normalizedFactors_cyclotomic_cardproof · cited by 0