Theorems · Theorem · order theory
Set.Ico_eq_empty_of_le
∀ {α : Type u_1} [inst : Preorder α] {a b : α}, b ≤ a → Set.Ico a b = ∅- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- Set.Icostatement · cited by 799
- LE.le.not_gtproof · cited by 189
- Set.Ico_eq_emptyproof · cited by 24
Cited by1
Results whose statement or proof uses this declaration.
- Monotone.biUnion_Ico_Ioc_map_succproof · cited by 0