Theorems · Theorem · order theory
iInter_Iio_of_not_bddBelow_range
∀ {ι : Sort u} {α : Type v} [inst : LinearOrder α] {f : ι → α}, ¬BddBelow (Set.range f) → ⋂ i, Set.Iio (f i) = ∅- Defined in
- Mathlib.Order.Interval.Set.Disjoint
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrder
Around this declaration
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Cites10
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.rangestatement and proof · cited by 4,705
- Set.Iiostatement and proof · cited by 1,166
- Set.iInterstatement and proof · cited by 1,084
- BddBelowstatement and proof · cited by 401
- Set.Iio_subset_Iic_selfproof · cited by 21
- Set.eq_empty_of_subset_emptyproof · cited by 15
- Set.iInter_mono''proof · cited by 3
- iInter_Iic_eq_empty_iffproof · cited by 2
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