Theorems · Theorem · order theory
Finset.Icc_eq_empty_iff
∀ {α : Type u_2} {a b : α} [inst : Preorder α] [inst_1 : LocallyFiniteOrder α], Finset.Icc a b = ∅ ↔ ¬a ≤ b- Defined in
- Mathlib.Order.Interval.Finset.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 59 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Finsetstatement · cited by 13,712
- Preorderstatement and proof · cited by 7,952
- LocallyFiniteOrderstatement and proof · cited by 658
- Finset.Iccstatement · cited by 348
- Finset.coe_Iccproof · cited by 60
- Finset.coe_eq_emptyproof · cited by 8
- Set.Icc_eq_empty_iffproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Finset.Icc_eq_emptyproof · cited by 3
- Multiset.Icc_eq_zero_iffproof · cited by 1