Theorems · Theorem · order theory
Finset.Ioc_eq_empty_of_le
∀ {α : Type u_2} {a b : α} [inst : Preorder α] [inst_1 : LocallyFiniteOrder α], b ≤ a → Finset.Ioc a b = ∅- Defined in
- Mathlib.Order.Interval.Finset.Basic
- Cited by
- 5 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.Iocstatement · cited by 301
- LE.le.not_gtproof · cited by 189
- Finset.Ioc_eq_emptyproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- sum_mul_eq_sub_sub_integral_mulproof · cited by 4
- MeasureTheory.partialTraj_const_restrict₂proof · cited by 1
- sup_Ioc_disjointed_of_monotoneproof · cited by 1
- schnirelmannDensity_mul_le_card_filterproof · cited by 1
- Nat.Ioc_filter_dvd_card_eq_divproof · cited by 0