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Theorems · Theorem · order theory

LowerAdjoint.le_iff_subset

∀ {α : Type u_1} {β : Type u_4} [inst : SetLike α β] [inst_1 : Preorder α] (l : LowerAdjoint SetLike.coe) (s : Set β)
  (S : α), l.toFun s ≤ S ↔ s ⊆ ↑S
Defined in
Mathlib.Order.Closure
Cited by
2 results in Mathlib
Foundations
Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SetLikePreorder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

LowerAdjoint.eq_of_le · cited by 2LowerAdjoint.eq_of_leLowerAdjoint.mem_iff · cited by 0LowerAdjoint.mem_iffSet · cited by 53352SetSetLike.coe · cited by 8199SetLike.coePreorder · cited by 7952PreorderSetLike · cited by 1084SetLikeLowerAdjoint.toFun · cited by 105LowerAdjoint.toFunLowerAdjoint · cited by 38LowerAdjointLowerAdjoint.gc · cited by 3LowerAdjoint.gcLowerAdjoint.le_iff_subsetCITED BYCITES

Cites7

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.