Theorems · Theorem · combinatorics
Multiset.card_product
∀ {α : Type u_1} {β : Type v} (s : Multiset α) (t : Multiset β), (s ×ˢ t).card = s.card * t.card- Defined in
- Mathlib.Data.Multiset.Bind
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- SProd.sprodstatement · cited by 1,750
- Multiset.mapproof · cited by 876
- Multiset.sumproof · cited by 388
- Multiset.cardstatement and proof · cited by 375
- Multiset.map_congrproof · cited by 232
- Multiset.card_mapproof · cited by 57
- Multiset.map_const'proof · cited by 39
- Multiset.sum_replicateproof · cited by 30
- Multiset.card_bindproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- Finset.card_productproof · cited by 39
- Polynomial.resultant_eq_prod_roots_subproof · cited by 1
- Polynomial.map_sub_roots_sprod_eq_prod_map_evalproof · cited by 1