Theorems · Theorem · order theory
LowerAdjoint.closure_top
∀ {α : Type u_1} {β : Type u_4} [inst : PartialOrder α] [inst_1 : OrderTop α] [inst_2 : Preorder β] {u : β → α}
(l : LowerAdjoint u), u (l.toFun ⊤) = ⊤- Defined in
- Mathlib.Order.Closure
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
- Assumes
- PartialOrderOrderTopPreorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement · cited by 9,680
- Preorderstatement and proof · cited by 7,952
- PartialOrderstatement and proof · cited by 6,410
- OrderTopstatement and proof · cited by 493
- LowerAdjoint.toFunstatement · cited by 105
- LowerAdjointstatement and proof · cited by 38
- LowerAdjoint.closureOperatorproof · cited by 12
- ClosureOperator.closure_topproof · cited by 4
Cited by0
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