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Theorems · Theorem · order theory

IsLowerSet.compl

∀ {α : Type u_1} [inst : LE α] {s : Set α}, IsLowerSet s → IsUpperSet sᶜ
Defined in
Mathlib.Order.UpperLower.Basic
Cited by
7 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms
Assumes
LE
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Around this declaration

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

isLowerSet_compl · cited by 6isLowerSet_complisUpperSet_compl · cited by 5isUpperSet_complIsLowerSet.dirSupInaccOn · cited by 2IsLowerSet.dirSupInaccOnIsLowerSet.eq_univ_or_Iio · cited by 2IsLowerSet.eq_univ_or_IioIsLowerSet.dirSupInacc · cited by 1IsLowerSet.dirSupInaccIsLowerSet.isOpen · cited by 1IsLowerSet.isOpenIsLowerSet.null_frontier · cited by 1IsLowerSet.null_frontierSet · cited by 53352SetCompl.compl · cited by 2925Compl.complIsLowerSet · cited by 167IsLowerSetIsUpperSet · cited by 148IsUpperSetIsLowerSet.complCITED BYCITES

Cites4

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

Cited by7

Results whose statement or proof uses this declaration.