Theorems · Theorem · order theory
Multiset.finsetSum_eq_sup_iff_disjoint
∀ {α : Type u_2} {β : Type u_3} [inst : DecidableEq α] {i : Finset β} {f : β → Multiset α},
i.sum f = i.sup f ↔ ∀ x ∈ i, ∀ y ∈ i, x ≠ y → Disjoint (f x) (f y)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 65 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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidproof · cited by 12,281
- Finset.sumstatement and proof · cited by 5,195
- Multisetstatement and proof · cited by 2,627
- Disjointstatement and proof · cited by 2,201
- Finset.supstatement and proof · cited by 530
- Finset.consproof · cited by 221
- Finset.sum_consproof · cited by 84
- Finset.sup_emptyproof · cited by 72
- Finset.sup_leproof · cited by 44
- Finset.cons_induction_onproof · cited by 37
- Finset.sup_consproof · cited by 30
Cited by2
Results whose statement or proof uses this declaration.
- Multiset.sup_powerset_lenproof · cited by 0
- Multiset.finset_sum_eq_sup_iff_disjointproof · cited by 0