Theorems · Theorem · combinatorics
Multiset.countP_map
∀ {α : Type u_1} {β : Type v} (f : α → β) (s : Multiset α) (p : β → Prop) [inst : DecidablePred p],
Multiset.countP p (Multiset.map f s) = (Multiset.filter (fun a => p (f a)) s).card- Defined in
- Mathlib.Data.Multiset.Filter
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Quot.sound
- Assumes
- DecidablePred
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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.mapstatement and proof · cited by 876
- Multiset.cardstatement and proof · cited by 375
- Multiset.consproof · cited by 313
- Multiset.induction_onproof · cited by 109
- Multiset.filterstatement and proof · cited by 102
- Multiset.map_consproof · cited by 93
- Multiset.countPstatement and proof · cited by 28
- Multiset.card_singletonproof · cited by 17
- Multiset.card_addproof · cited by 8
- Multiset.map_zeroproof · cited by 8
- Multiset.filter_consproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- Multiset.count_mapproof · cited by 4
- Multiset.count_map_eq_countproof · cited by 1