Theorems · Theorem · order theory
Set.unbounded_le_inter_le
∀ {α : Type u_1} {s : Set α} [inst : LinearOrder α] (a : α),
Set.Unbounded (fun x1 x2 => x1 ≤ x2) (s ∩ {b | a ≤ b}) ↔ Set.Unbounded (fun x1 x2 => x1 ≤ x2) s- Defined in
- Mathlib.Order.Bounded
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrder
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.
- Setstatement and proof · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- Set.ofPredstatement and proof · cited by 6,101
- not_iff_notproof · cited by 159
- Set.Boundedproof · cited by 57
- Set.Unboundedstatement and proof · cited by 39
- Set.not_bounded_iffproof · cited by 7
- Set.bounded_le_inter_leproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Set.unbounded_ge_iff_unbounded_inter_geproof · cited by 0