Theorems · Theorem · order theory
Set.Iio_inter_Iio
∀ {α : Type u_1} [inst : LinearOrder α] {a b : α}, Set.Iio a ∩ Set.Iio b = Set.Iio (min a b)- Defined in
- Mathlib.Order.Interval.Set.LinearOrder
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
- Assumes
- LinearOrder
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
- LinearOrderstatement and proof · cited by 8,572
- Set.extproof · cited by 2,266
- Set.Iiostatement · cited by 1,166
- lt_inf_iffproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- isPiSystem_image_Iioproof · cited by 3
- Topology.IsLower.isTopologicalBasis_insert_univ_subbasisproof · cited by 2