Theorems · Theorem · order theory
Multiset.le_sum_of_mem
∀ {α : Type u_2} [inst : AddCommMonoid α] {m : Multiset α} {a : α},
a ∈ m → ∀ [inst_1 : Preorder α] [CanonicallyOrderedAdd α], a ≤ m.sum- Cited by
- 5 results in Mathlib
- Foundations
- Depth 16 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
- Multiset.sumstatement · cited by 388
- Multiset.consproof · cited by 313
- CanonicallyOrderedAddstatement and proof · cited by 229
- Multiset.sum_consproof · cited by 45
- le_add_rightproof · cited by 21
- Multiset.exists_cons_of_memproof · cited by 15
Cited by5
Results whose statement or proof uses this declaration.
- Multiset.finsetSum_eq_sup_iff_disjointproof · cited by 2
- Nat.Partition.partition_one_partsproof · cited by 1
- Equiv.Perm.le_card_support_of_mem_cycleTypeproof · cited by 1
- alternatingGroup.mem_kleinFour_of_order_two_powproof · cited by 1
- Nat.Partition.le_of_mem_partsproof · cited by 0