Theorems · Theorem · combinatorics
Multiset.card_lt_card
∀ {α : Type u_1} {s t : Multiset α}, s < t → s.card < t.card- Defined in
- Mathlib.Data.Multiset.Defs
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- le_of_ltproof · cited by 1,175
- Multiset.cardstatement and proof · cited by 375
- lt_of_not_geproof · cited by 374
- ne_of_ltproof · cited by 203
- Multiset.eq_of_le_of_card_leproof · cited by 11
Cited by6
Results whose statement or proof uses this declaration.
- Finset.card_lt_cardproof · cited by 23
- Multiset.lt_iff_cons_leproof · cited by 3
- Multiset.covBy_consproof · cited by 1
- Finsupp.sum_id_lt_of_ltproof · cited by 1
- Multiset.card_erase_lt_of_memproof · cited by 1
- Multiset.card_strictMonoproof · cited by 0