Theorems · Theorem · combinatorics
Multiset.bind_singleton
∀ {α : Type u_1} {β : Type v} (s : Multiset α) (f : α → β), (s.bind fun x => {f x}) = Multiset.map f s- Defined in
- Mathlib.Data.Multiset.Bind
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.induction_onproof · cited by 109
- Multiset.map_consproof · cited by 93
- Multiset.bindstatement and proof · cited by 59
- Multiset.cons_bindproof · cited by 13
- Multiset.map_zeroproof · cited by 8
- Multiset.zero_bindproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- LinearMap.IsSymmetric.roots_charpoly_eq_eigenvaluesproof · cited by 4
- Matrix.IsHermitian.roots_charpoly_eq_eigenvaluesproof · cited by 4
- Polynomial.roots_multiset_prod_X_sub_Cproof · cited by 3
- Polynomial.roots_prod_X_sub_Cproof · cited by 2
- Multiset.product_singletonproof · cited by 0