Theorems · Theorem · order theory
Fintype.sum_eq_zero_iff_of_nonneg
∀ {ι : Type u_9} {M : Type u_10} [inst : Fintype ι] [inst_1 : AddCommMonoid M] [inst_2 : PartialOrder M] [AddLeftMono M]
{f : ι → M}, 0 ≤ f → (∑ i, f i = 0 ↔ f = 0)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, 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
- Fintypestatement and proof · cited by 7,736
- PartialOrderstatement and proof · cited by 6,410
- Finset.sumstatement · cited by 5,195
- Finset.univstatement and proof · cited by 3,473
- AddLeftMonostatement and proof · cited by 687
- Finset.mem_univproof · cited by 361
- Finset.sum_eq_zero_iff_of_nonnegproof · cited by 19
Cited by3
Results whose statement or proof uses this declaration.
- dotProduct_star_self_eq_zeroproof · cited by 2
- dotProduct_self_star_eq_zeroproof · cited by 1
- holleyproof · cited by 0