Theorems · Theorem · order theory
iInter_Iic_eq_empty_iff
∀ {ι : Sort u} {α : Type v} [inst : LinearOrder α] {f : ι → α}, ⋂ i, Set.Iic (f i) = ∅ ↔ ¬BddBelow (Set.range f)- Defined in
- Mathlib.Order.Interval.Set.Disjoint
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 25 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- Set.rangestatement · cited by 4,705
- Set.Iicstatement · cited by 1,111
- Set.iInterstatement · cited by 1,084
- BddBelowstatement · cited by 401
Cited by2
Results whose statement or proof uses this declaration.
- Real.iInter_Iic_ratproof · cited by 1
- iInter_Iio_of_not_bddBelow_rangeproof · cited by 0