Theorems · Theorem · order theory
Fintype.sum_pos_iff_of_nonneg
∀ {ι : Type u_1} {M : Type u_4} [inst : Fintype ι] [inst_1 : AddCommMonoid M] [inst_2 : PartialOrder M]
[IsOrderedCancelAddMonoid M] {f : ι → M}, 0 ≤ f → (0 < ∑ i, f i ↔ 0 < f)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Finset.sum_congrproof · cited by 2,323
- IsOrderedCancelAddMonoidstatement and proof · cited by 359
- LE.le.eq_or_ltproof · cited by 220
- Finset.sum_const_zeroproof · cited by 219
- lt_self_iff_falseproof · cited by 41
- Fintype.sum_posproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.dotProduct_star_self_pos_iffproof · cited by 1