Theorems · Theorem · order theory
Multiset.sum_le_sum_of_rel_le
∀ {α : Type u_2} [inst : AddCommMonoid α] [inst_1 : Preorder α] {s t : Multiset α} [AddLeftMono α],
Multiset.Rel (fun x1 x2 => x1 ≤ x2) s t → s.sum ≤ t.sum- Cited by
- 2 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- le_reflproof · cited by 2,061
- AddLeftMonostatement and proof · cited by 687
- add_le_addproof · cited by 666
- Multiset.sumstatement and proof · cited by 388
- Multiset.consproof · cited by 313
- Multiset.Relstatement and proof · cited by 47
- Multiset.sum_consproof · cited by 45
Cited by2
Results whose statement or proof uses this declaration.
- Multiset.sum_map_le_sumproof · cited by 2
- Multiset.sum_map_le_sum_mapproof · cited by 1