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Theorems · Theorem · order theory

Set.Ici_disjoint_Iic

∀ {α : Type v} [inst : Preorder α] {a b : α}, Disjoint (Set.Ici a) (Set.Iic b) ↔ ¬a ≤ b
Defined in
Mathlib.Order.Interval.Set.Disjoint
Cited by
1 results in Mathlib
Foundations
Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Preorder
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Filter.disjoint_atTop_atBot · cited by 2Filter.disjoint_atTop_atB…Set · cited by 53352SetPreorder · cited by 7952PreorderDisjoint · cited by 2201DisjointSet.Iic · cited by 1111Set.IicSet.Ici · cited by 1070Set.IciSet.disjoint_iff_inter_eq_empty · cited by 49Set.disjoint_iff_inter_eq…Set.Ici_inter_Iic · cited by 12Set.Ici_inter_IicSet.Icc_eq_empty_iff · cited by 4Set.Icc_eq_empty_iffSet.Ici_disjoint_IicCITED BYCITES

Cites8

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Cited by1

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