Theorems · Theorem · order theory
Finset.Ico_eq_empty_of_le
∀ {α : Type u_2} {a b : α} [inst : Preorder α] [inst_1 : LocallyFiniteOrder α], b ≤ a → Finset.Ico a b = ∅- Defined in
- Mathlib.Order.Interval.Finset.Basic
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderLocallyFiniteOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- Preorderstatement and proof · cited by 7,952
- LocallyFiniteOrderstatement and proof · cited by 658
- Finset.Icostatement · cited by 450
- LE.le.not_gtproof · cited by 189
- Finset.Ico_eq_emptyproof · cited by 5
Cited by22
Results whose statement or proof uses this declaration.
- Nat.mem_divisorsproof · cited by 22
- Nat.mem_properDivisorsproof · cited by 15
- Finset.sum_Ico_eq_sum_rangeproof · cited by 10
- intervalIntegral.sum_integral_adjacent_intervals_Icoproof · cited by 4
- AntitoneOn.sum_Ico_le_integralproof · cited by 3
- LocallyFiniteOrder.orderAddMonoidHom_strictMonoproof · cited by 3
- Nat.geom_sum_Ico_leproof · cited by 2
- eVariationOn.sum_le_of_monotoneOn_Iccproof · cited by 2
- Finset.le_sum_schlomilch'proof · cited by 2
- Finset.prod_Ico_reflectproof · cited by 2
- Finset.sum_schlomilch_le'proof · cited by 2
- FormalMultilinearSeries.radius_rightInv_pos_of_radius_posproof · cited by 1