Theorems · Theorem · order theory
Finset.sum_neg
∀ {ι : Type u_1} {M : Type u_4} [inst : AddCommMonoid M] [inst_1 : Preorder M] [IsOrderedCancelAddMonoid M] {f : ι → M}
{s : Finset ι} [AddLeftStrictMono M], (∀ i ∈ s, f i < 0) → s.Nonempty → ∑ i ∈ s, f i < 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 59 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.
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Preorderstatement and proof · cited by 7,952
- Finset.sumstatement · cited by 5,195
- le_reflproof · cited by 2,061
- Finset.Nonemptystatement and proof · cited by 1,001
- LT.lt.trans_leproof · cited by 678
- IsOrderedCancelAddMonoidstatement and proof · cited by 359
- Finset.sum_const_zeroproof · cited by 219
- AddLeftStrictMonostatement and proof · cited by 203
- Finset.sum_lt_sum_of_nonemptyproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- sign_sumproof · cited by 1