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Theorems · Theorem · order theory

OrderHom.sSup_apply

∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : CompleteLattice β] (s : Set (α →o β)) (x : α),
  (sSup s) x = ⨆ f ∈ s, f x
Defined in
Mathlib.Order.Hom.Order
Cited by
1 results in Mathlib
Foundations
Depth 16 from the axioms · uses no axioms
Assumes
PreorderCompleteLattice
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Around this declaration

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

OrderHom.iSup_apply · cited by 1OrderHom.iSup_applyDFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetPreorder · cited by 7952PreorderiSup · cited by 2415iSupCompleteLattice · cited by 1048CompleteLatticeSupSet.sSup · cited by 954SupSet.sSupOrderHom · cited by 934OrderHomOrderHom.sSup_applyCITED BYCITES

Cites7

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Cited by1

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