Theorems · Theorem · order theory
Finset.sum_le_sum_of_subset
∀ {ι : Type u_1} {M : Type u_4} [inst : AddCommMonoid M] [inst_1 : Preorder M] [CanonicallyOrderedAdd M] {f : ι → M}
{s t : Finset ι}, s ⊆ t → ∑ x ∈ s, f x ≤ ∑ x ∈ t, f x- Cited by
- 14 results in Mathlib
- Foundations
- Depth 66 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
- zero_leproof · cited by 382
- CanonicallyOrderedAddstatement and proof · cited by 229
- Finset.sum_le_sum_of_subset_of_nonnegproof · cited by 31
- CanonicallyOrderedAdd.toIsOrderedAddMonoidproof · cited by 5
Cited by14
Results whose statement or proof uses this declaration.
- MeasureTheory.lintegral_tsumproof · cited by 12
- Finset.sum_mono_setproof · cited by 6
- Finsupp.degree_monoproof · cited by 5
- Finset.sum_le_sum_of_ne_zeroproof · cited by 2
- ENNReal.hasSumproof · cited by 2
- ENNReal.hasSum_iff_tendsto_natproof · cited by 2
- MeasureTheory.VectorMeasure.le_variationproof · cited by 1
- MeasureTheory.preVariation.sum_le_preVariationFun_of_subsetproof · cited by 1
- Nat.geomSum_ltproof · cited by 1
- MeasureTheory.preVariation.sum_le_preVariationFun_iUnion'proof · cited by 1
- Nat.Prime.not_pseudoperfectproof · cited by 1
- Nat.abundancyIndex_le_of_dvdproof · cited by 1