Mathlib Map

Theorems · Theorem · order theory

OrderHom.iSup_apply

∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] {ι : Sort u_3} [inst_1 : CompleteLattice β] (f : ι → α →o β)
  (x : α), (⨆ i, f i) x = ⨆ i, (f i) x
Defined in
Mathlib.Order.Hom.Order
Cited by
1 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Quot.sound
Assumes
PreorderCompleteLattice
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

OrderHom.coe_iSup · cited by 0OrderHom.coe_iSupDFunLike.coe · cited by 62936DFunLike.coePreorder · cited by 7952PreorderSet.range · cited by 4705Set.rangeiSup · cited by 2415iSupCompleteLattice · cited by 1048CompleteLatticeOrderHom · cited by 934OrderHomiSup_range · cited by 24iSup_rangeOrderHom.sSup_apply · cited by 1OrderHom.sSup_applyOrderHom.iSup_applyCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.