Theorems · Theorem · order theory
Finset.single_le_sum_of_canonicallyOrdered
∀ {ι : Type u_1} {M : Type u_4} [inst : AddCommMonoid M] [inst_1 : Preorder M] [CanonicallyOrderedAdd M] {f : ι → M}
{s : Finset ι} {i : ι}, i ∈ s → f i ≤ ∑ j ∈ s, f jIn a canonically-ordered additive monoid, a sum bounds each of its terms.
See also Finset.single_le_sum.
- Cited by
- 2 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
- zero_leproof · cited by 382
- CanonicallyOrderedAddstatement and proof · cited by 229
- Finset.single_le_sumproof · cited by 34
- CanonicallyOrderedAdd.toIsOrderedAddMonoidproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- MvPowerSeries.truncTotal_subst_eq_truncTotal_subst_truncTotal_of_leproof · cited by 1
- Finsupp.le_degreeproof · cited by 1