Theorems · Definition · combinatorics
Multiset.join
{α : Type u_1} → Multiset (Multiset α) → Multiset αjoin S, where S is a multiset of multisets, is the lift of the list join
operation, that is, the union of all the sets.
For example, join {{1, 2}, {1, 2}, {0, 1}} = {0, 1, 1, 1, 2, 2}.
- Defined in
- Mathlib.Data.Multiset.Bind
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Multisetstatement · cited by 2,627
- Multiset.sumproof · cited by 388
Cited by22
Results whose statement or proof uses this declaration.
- Multiset.bindproof · cited by 59
- Multiset.bind_congrproof · cited by 15
- Multiset.cons_bindproof · cited by 13
- Multiset.join_consstatement · cited by 9
- Multiset.map_bindproof · cited by 6
- Multiset.coe_bindproof · cited by 5
- Multiset.add_bindproof · cited by 4
- Multiset.filter_joinstatement and proof · cited by 1
- Multiset.singleton_joinstatement · cited by 1
- Multiset.prod_joinstatement and proof · cited by 1
- Multiset.card_joinstatement and proof · cited by 1
- Multiset.attach_bind_coeproof · cited by 1