Theorems · Theorem · order theory
Finset.sum_pos_iff
∀ {ι : Type u_9} {M : Type u_10} [inst : AddCommMonoid M] [inst_1 : PartialOrder M] [CanonicallyOrderedAdd M]
{f : ι → M} {s : Finset ι}, 0 < ∑ x ∈ s, f x ↔ ∃ x ∈ s, 0 < f x- Cited by
- 0 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- Finset.sumstatement · cited by 5,195
- IsOrderedAddMonoidproof · cited by 1,659
- zero_leproof · cited by 382
- CanonicallyOrderedAddstatement and proof · cited by 229
- CanonicallyOrderedAdd.toIsOrderedAddMonoidproof · cited by 5
- Finset.sum_pos_iff_of_nonnegproof · cited by 3
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