Theorems · Theorem · order theory
Multiset.le_sum_of_subadditive
∀ {α : Type u_2} {β : Type u_3} [inst : AddCommMonoid α] [inst_1 : AddCommMonoid β] [inst_2 : Preorder β]
[IsOrderedAddMonoid β] (f : α → β),
f 0 ≤ 0 → (∀ (a b : α), f (a + b) ≤ f a + f b) → ∀ (s : Multiset α), f s.sum ≤ (Multiset.map f s).sum- Cited by
- 4 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- Preorderstatement and proof · cited by 7,952
- Multisetstatement and proof · cited by 2,627
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- Multiset.mapstatement · cited by 876
- Multiset.sumstatement · cited by 388
- List.le_sum_of_subadditiveproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- Finset.le_sum_of_subadditiveproof · cited by 6
- norm_multiset_sum_leproof · cited by 3
- enorm_multisetSum_leproof · cited by 0
- Multiset.abs_sum_le_sum_absproof · cited by 0