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Theorems · Theorem · order theory

Set.iUnion_Ioi

∀ {α : Type v} [inst : Preorder α] [NoMinOrder α], ⋃ a, Set.Ioi a = Set.univ
Defined in
Mathlib.Order.Interval.Set.Disjoint
Cited by
2 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Quot.sound
Assumes
PreorderNoMinOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Set.iUnion_Ioc_left · cited by 1Set.iUnion_Ioc_leftSet.iUnion_Ioo_left · cited by 0Set.iUnion_Ioo_leftSet · cited by 53352SetPreorder · cited by 7952PreorderSet.univ · cited by 3945Set.univSet.iUnion · cited by 2483Set.iUnionSet.Ioi · cited by 1463Set.IoiNoMinOrder · cited by 247NoMinOrderNoMinOrder.exists_lt · cited by 41NoMinOrder.exists_ltSet.iUnion_eq_univ_iff · cited by 19Set.iUnion_eq_univ_iffSet.iUnion_IoiCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.