Theorems · Theorem · combinatorics
Multiset.card_pi
∀ {α : Type u_1} [inst : DecidableEq α] {β : α → Type u_2} (m : Multiset α) (t : (a : α) → Multiset (β a)),
(m.pi t).card = (Multiset.map (fun a => (t a).card) m).prod- Defined in
- Mathlib.Data.Multiset.Pi
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 62 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.
Cites18
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.prodstatement and proof · cited by 528
- Multiset.sumproof · cited by 388
- Multiset.cardstatement and proof · cited by 375
- Multiset.map_congrproof · cited by 232
- Multiset.induction_onproof · cited by 109
- Multiset.map_consproof · cited by 93
- Multiset.prod_consproof · cited by 68
- Multiset.card_mapproof · cited by 57
- Multiset.map_const'proof · cited by 39
- Multiset.sum_replicateproof · cited by 30
Cited by1
Results whose statement or proof uses this declaration.
- Finset.card_piproof · cited by 4