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Theorems · Theorem · order theory

isLowerSet_univ

∀ {α : Type u_1} [inst : LE α], IsLowerSet Set.univ
Defined in
Mathlib.Order.UpperLower.Basic
Cited by
8 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.

Topology.IsLower.isLowerSet_of_isOpen · cited by 4IsLower.isLowerSet_of_isO…Topology.scottHausdorff_le_lower · cited by 2Topology.scottHausdorff_l…stableUnderSpecialization_univ · cited by 1stableUnderSpecialization…DirSupClosed.union · cited by 1DirSupClosed.unionTopology.IsScottHausdorff.isClosed_iff_dirSupClosed · cited by 0IsScottHausdorff.isClosed…dirSupInacc_iff_inter_subset · cited by 0dirSupInacc_iff_inter_sub…DirSupInacc.inter · cited by 0DirSupInacc.interTopology.IsScottHausdorff.isOpen_iff_dirSupInacc · cited by 0IsScottHausdorff.isOpen_i…Set.univ · cited by 3945Set.univIsLowerSet · cited by 167IsLowerSetisLowerSet_univCITED BYCITES

Cites2

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

Cited by8

Results whose statement or proof uses this declaration.