Theorems · Theorem · order theory
Multiset.sum_map_le_sum
∀ {α : Type u_2} [inst : AddCommMonoid α] [inst_1 : Preorder α] {s : Multiset α} [AddLeftMono α] (f : α → α),
(∀ x ∈ s, f x ≤ x) → (Multiset.map f s).sum ≤ s.sum- Cited by
- 2 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- AddLeftMonostatement and proof · cited by 687
- Multiset.sumstatement · cited by 388
- Multiset.rel_refl_of_refl_onproof · cited by 5
- Multiset.rel_map_leftproof · cited by 4
- Multiset.sum_le_sum_of_rel_leproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Multiset.sum_le_sum_mapproof · cited by 0
- Multiset.card_nsmul_le_sumproof · cited by 0