Theorems · Theorem · order theory
Multiset.sum_eq_zero_iff
∀ {α : Type u_2} [inst : AddCommMonoid α] {m : Multiset α} [inst_1 : PartialOrder α] [CanonicallyOrderedAdd α]
[IsOrderedAddMonoid α], m.sum = 0 ↔ ∀ x ∈ m, x = 0- Cited by
- 2 results in Mathlib
- Foundations
- Depth 18 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
- PartialOrderstatement and proof · cited by 6,410
- Multisetstatement and proof · cited by 2,627
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- Multiset.sumstatement · cited by 388
- CanonicallyOrderedAddstatement and proof · cited by 229
- Multiset.mem_coeproof · cited by 17
- List.sum_eq_zero_iffproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Nat.Partition.partition_zero_partsproof · cited by 6
- alternatingGroup.mem_kleinFour_of_order_two_powproof · cited by 1