Theorems · Theorem · order theory
Finset.exists_pos_of_sum_zero_of_exists_nonzero
∀ {ι : Type u_1} {M : Type u_4} [inst : AddCommMonoid M] [inst_1 : LinearOrder M] {s : Finset ι}
[IsOrderedCancelAddMonoid M] (f : ι → M), ∑ i ∈ s, f i = 0 → (∃ i ∈ s, f i ≠ 0) → ∃ i ∈ s, 0 < f i- Cited by
- 3 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- LinearOrderstatement and proof · cited by 8,572
- Finset.sumstatement and proof · cited by 5,195
- IsOrderedCancelAddMonoidstatement and proof · cited by 359
- not_ltproof · cited by 306
- Finset.sum_const_zeroproof · cited by 219
- ne_of_ltproof · cited by 203
- LE.le.lt_of_neproof · cited by 116
- Finset.sum_lt_sumproof · cited by 11
Cited by3
Results whose statement or proof uses this declaration.
- Convex.radon_partitionproof · cited by 1
- Caratheodory.mem_convexHull_eraseproof · cited by 1