Theorems · Theorem · order theory
Finset.sum_mono_set
∀ {ι : Type u_1} {M : Type u_4} [inst : AddCommMonoid M] [inst_1 : Preorder M] [CanonicallyOrderedAdd M] (f : ι → M),
Monotone fun s => ∑ x ∈ s, f x- Cited by
- 6 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- Preorderstatement and proof · cited by 7,952
- Finset.sumstatement · cited by 5,195
- IsOrderedAddMonoidproof · cited by 1,659
- Monotonestatement · cited by 1,397
- CanonicallyOrderedAddstatement and proof · cited by 229
- Finset.sum_le_sum_of_subsetproof · cited by 14
- CanonicallyOrderedAdd.toIsOrderedAddMonoidproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- ENNReal.tsum_eq_iSup_sum'proof · cited by 2
- hasSum_of_isLUBproof · cited by 2
- eVariationOn.sum_le_of_monotoneOn_Iccproof · cited by 2
- NNReal.not_summable_iff_tendsto_nat_atTopproof · cited by 2
- Finset.sum_le_one_iffproof · cited by 1
- isLUB_hasSum'proof · cited by 0