Theorems · Theorem · number theory
Finset.sum_Ico_le_sum
∀ {s : Finset ℤ} {c : ℤ}, (∀ x ∈ s, c ≤ x) → ∑ x ∈ Finset.Ico c (c + ↑s.card), x ≤ ∑ x ∈ s, xSharp lower bound for the sum of a finset of integers that is bounded below, Ico version.
- Defined in
- Mathlib.Algebra.Order.Group.Int.Sum
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- Finset.sumstatement and proof · cited by 5,195
- Finset.cardstatement and proof · cited by 2,327
- LT.lt.leproof · cited by 2,189
- le_reflproof · cited by 2,061
- add_le_addproof · cited by 666
- le_imp_le_of_le_of_leproof · cited by 576
- Finset.Icostatement and proof · cited by 450
- add_sub_cancel_leftproof · cited by 198
- Finset.mem_Icoproof · cited by 50
- Finset.mem_sdiffproof · cited by 44
- Finset.inter_commproof · cited by 25
Cited by1
Results whose statement or proof uses this declaration.
- Finset.sum_range_le_sumproof · cited by 0