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Theorems · Theorem · order theory

OrderIso.map_sSup

∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLattice α] [inst_1 : CompleteLattice β] (f : α ≃o β) (s : Set α),
  f (sSup s) = ⨆ a ∈ s, f a
Defined in
Mathlib.Order.CompleteLattice.Basic
Cited by
3 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Quot.sound
Assumes
CompleteLatticeCompleteLattice
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

OrderIso.map_sSup_eq_sSup_symm_preimage · cited by 18OrderIso.map_sSup_eq_sSup…sInf_inv · cited by 1sInf_invsInf_neg · cited by 1sInf_negDFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetiSup · cited by 2415iSupCompleteLattice · cited by 1048CompleteLatticeSupSet.sSup · cited by 954SupSet.sSupOrderIso · cited by 874OrderIsosSup_eq_iSup · cited by 42sSup_eq_iSupOrderIso.map_iSup · cited by 25OrderIso.map_iSupOrderIso.map_sSupCITED BYCITES

Cites8

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Cited by3

Results whose statement or proof uses this declaration.