Theorems · Theorem · order theory
Finset.exists_le_of_sum_le
∀ {ι : Type u_1} {M : Type u_4} [inst : AddCommMonoid M] [inst_1 : LinearOrder M] {f g : ι → M} {s : Finset ι}
[IsOrderedCancelAddMonoid M], s.Nonempty → ∑ i ∈ s, f i ≤ ∑ i ∈ s, g i → ∃ i ∈ s, f i ≤ g i- Cited by
- 3 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.
Cites8
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
- Finset.Nonemptystatement and proof · cited by 1,001
- IsOrderedCancelAddMonoidstatement and proof · cited by 359
- not_leproof · cited by 328
- Finset.sum_lt_sum_of_nonemptyproof · cited by 10
Cited by3
Results whose statement or proof uses this declaration.
- Finset.exists_le_sum_fiber_of_maps_to_of_nsmul_le_sumproof · cited by 3
- ConvexOn.exists_ge_of_centerMassproof · cited by 2
- Finset.exists_le_sum_fiber_of_sum_fiber_nonpos_of_nsmul_le_sumproof · cited by 1