Theorems · Theorem · order theory
Finset.exists_lt_of_sum_lt
∀ {ι : Type u_1} {M : Type u_4} [inst : AddCommMonoid M] [inst_1 : LinearOrder M] {f g : ι → M} {s : Finset ι}
[AddLeftMono M], ∑ i ∈ s, f i < ∑ i ∈ s, g i → ∃ i ∈ s, f i < g i- Cited by
- 2 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- AddLeftMonostatement and proof · cited by 687
- not_ltproof · cited by 306
- Finset.sum_le_sumproof · cited by 182
Cited by2
Results whose statement or proof uses this declaration.
- Finset.exists_lt_sum_fiber_of_maps_to_of_nsmul_lt_sumproof · cited by 3
- Finset.exists_lt_sum_fiber_of_sum_fiber_nonpos_of_nsmul_lt_sumproof · cited by 1