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Theorems · Theorem · order theory

LowerAdjoint.closure_is_closed

∀ {α : Type u_1} {β : Type u_4} [inst : PartialOrder α] [inst_1 : Preorder β] {u : β → α} (l : LowerAdjoint u) (x : α),
  u (l.toFun x) ∈ l.closed
Defined in
Mathlib.Order.Closure
Cited by
0 results in Mathlib
Foundations
Depth 16 from the axioms · uses propext, Quot.sound
Assumes
PartialOrderPreorder
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Around this declaration

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

LowerAdjoint.toClosed · cited by 0LowerAdjoint.toClosedSet · cited by 53352SetPreorder · cited by 7952PreorderPartialOrder · cited by 6410PartialOrderLowerAdjoint.toFun · cited by 105LowerAdjoint.toFunLowerAdjoint · cited by 38LowerAdjointLowerAdjoint.closed · cited by 9LowerAdjoint.closedLowerAdjoint.idempotent · cited by 1LowerAdjoint.idempotentLowerAdjoint.closure_is_closedCITED BYCITES

Cites7

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Cited by1

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