Theorems · Theorem · order theory
List.sum_eq_zero_iff
∀ {M : Type u_3} [inst : AddCommMonoid M] [inst_1 : PartialOrder M] [IsOrderedAddMonoid M] [CanonicallyOrderedAdd M]
{l : List M}, l.sum = 0 ↔ ∀ x ∈ l, x = 0- Cited by
- 2 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
- PartialOrderstatement and proof · cited by 6,410
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- zero_leproof · cited by 382
- CanonicallyOrderedAddstatement and proof · cited by 229
- nsmul_zeroproof · cited by 73
- List.sum_replicateproof · cited by 19
- List.all_zero_of_le_zero_le_of_sum_eq_zeroproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Multiset.sum_eq_zero_iffproof · cited by 2
- PseudoMetricSpace.le_two_mul_dist_ofPreNNDistproof · cited by 1