Mathlib Map

Theorems · Definition · order theory

UpperSet.compl

{α : Type u_1} → [inst : LE α] → UpperSet α → LowerSet α

The complement of an upper set as a lower set.

Defined in
Mathlib.Order.UpperLower.CompleteLattice
Cited by
17 results in Mathlib
Foundations
Depth 12 from the axioms · uses no axioms
Assumes
LE
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

upperSetIsoLowerSet · cited by 2upperSetIsoLowerSetUpperSet.compl_iInf · cited by 1UpperSet.compl_iInfUpperSet.compl_iSup · cited by 1UpperSet.compl_iSupLowerSet.compl_compl · cited by 0LowerSet.compl_complupperSetIsoLowerSet_apply · cited by 0upperSetIsoLowerSet_applyUpperSet.compl_bot · cited by 0UpperSet.compl_botUpperSet.compl_compl · cited by 0UpperSet.compl_complUpperSet.compl_iInf₂ · cited by 0UpperSet.compl_iInf₂UpperSet.compl_iSup₂ · cited by 0UpperSet.compl_iSup₂UpperSet.compl_inf · cited by 0UpperSet.compl_infUpperSet.compl_le_compl · cited by 0UpperSet.compl_le_complUpperSet.compl_map · cited by 0UpperSet.compl_mapUpperSet.compl_sInf · cited by 0UpperSet.compl_sInfUpperSet.compl_sSup · cited by 0UpperSet.compl_sSupUpperSet.compl_sup · cited by 0UpperSet.compl_supSetLike.coe · cited by 8199SetLike.coeCompl.compl · cited by 2925Compl.complUpperSet · cited by 245UpperSetLowerSet · cited by 230LowerSetUpperSet.complCITED BYCITES

Cites4

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Cited by18

Results whose statement or proof uses this declaration.