Theorems · Theorem · order theory
LowerAdjoint.le_closure_iff
∀ {α : Type u_1} {β : Type u_4} [inst : PartialOrder α] [inst_1 : Preorder β] {u : β → α} (l : LowerAdjoint u)
(x y : α), x ≤ u (l.toFun y) ↔ u (l.toFun x) ≤ u (l.toFun y)- 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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Cites5
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
- PartialOrderstatement and proof · cited by 6,410
- LowerAdjoint.toFunstatement · cited by 105
- LowerAdjointstatement and proof · cited by 38
- ClosureOperator.le_closure_iffproof · cited by 5
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