Theorems · Definition · order theory
LowerAdjoint.toClosed
{α : Type u_1} →
{β : Type u_4} → [inst : PartialOrder α] → [inst_1 : Preorder β] → {u : β → α} → (l : LowerAdjoint u) → α → ↑l.closedSend an x to an element of the set of closed elements (by taking the closure).
- Defined in
- Mathlib.Order.Closure
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
- Assumes
- PartialOrderPreorder
Around this declaration
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- Set.Elemstatement · cited by 7,166
- PartialOrderstatement and proof · cited by 6,410
- LowerAdjoint.toFunproof · cited by 105
- LowerAdjointstatement and proof · cited by 38
- LowerAdjoint.closedstatement · cited by 9
- LowerAdjoint.closure_is_closedproof · cited by 0
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