Theorems · Theorem · combinatorics
Multiset.eq_of_le_of_card_le
∀ {α : Type u_1} {s t : Multiset α}, s ≤ t → t.card ≤ s.card → s = t- Defined in
- Mathlib.Data.Multiset.Defs
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.cardstatement and proof · cited by 375
- Multiset.ofListproof · cited by 290
- Multiset.leInductionOnproof · cited by 12
Cited by11
Results whose statement or proof uses this declaration.
- Finset.eq_of_subset_of_card_leproof · cited by 34
- Multiset.card_eq_zeroproof · cited by 13
- Multiset.card_lt_cardproof · cited by 6
- Multiset.map_lt_mapproof · cited by 3
- IsPrimitiveRoot.nthRoots_eqproof · cited by 3
- Polynomial.roots_eq_of_degree_le_card_of_ne_zeroproof · cited by 2
- Finset.injOn_of_card_image_eqproof · cited by 2
- Multiset.dedup_card_eq_card_iff_nodupproof · cited by 1
- Polynomial.roots_map_of_injective_of_card_eq_natDegreeproof · cited by 1
- Polynomial.roots_map_of_map_ne_zero_of_card_eq_natDegreeproof · cited by 1
- UniqueFactorizationMonoid.factors_eq_singleton_of_irreducibleproof · cited by 0