Theorems · Theorem · order theory
Multiset.sum_lt_sum
∀ {ι : Type u_1} {α : Type u_2} [inst : AddCommMonoid α] [inst_1 : Preorder α] [IsOrderedCancelAddMonoid α]
[AddLeftStrictMono α] {s : Multiset ι} {f g : ι → α},
(∀ i ∈ s, f i ≤ g i) → (∃ i ∈ s, f i < g i) → (Multiset.map f s).sum < (Multiset.map g s).sum- Cited by
- 3 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, 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.
- AddCommMonoidstatement and proof · cited by 12,281
- Preorderstatement and proof · cited by 7,952
- Multisetstatement and proof · cited by 2,627
- Multiset.mapstatement · cited by 876
- Multiset.sumstatement · cited by 388
- IsOrderedCancelAddMonoidstatement and proof · cited by 359
- AddLeftStrictMonostatement and proof · cited by 203
- List.sum_lt_sumproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Finset.sum_lt_sumproof · cited by 11
- Multiset.sum_lt_sum_of_nonemptyproof · cited by 1
- Function.HasMaxCutProperty.forbids_commutativeFractionalPolymorphismproof · cited by 0