Theorems · Theorem · order theory
sSup_image
∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLattice α] {s : Set β} {f : β → α}, sSup (f '' s) = ⨆ a ∈ s, f a- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 36 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
- Assumes
- CompleteLattice
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.
- Setstatement and proof · cited by 53,352
- Set.Elemproof · cited by 7,166
- Set.imagestatement and proof · cited by 5,609
- iSupstatement and proof · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- SupSet.sSupstatement and proof · cited by 954
- iSup_subtype''proof · cited by 18
- sSup_image'proof · cited by 10
Cited by36
Results whose statement or proof uses this declaration.
- Set.sUnion_imageproof · cited by 28
- OrderIso.map_sSup_eq_sSup_symm_preimageproof · cited by 18
- iSup_imageproof · cited by 12
- IsCompact.nhdsSet_prod_eqproof · cited by 5
- Filter.limsup_eq_iInf_iSupproof · cited by 5
- Filter.limsup_eq_iInf_iSup_of_natproof · cited by 5
- Filter.HasBasis.limsup_eq_iInf_iSupproof · cited by 5
- GaloisInsertion.l_sSup_u_imageproof · cited by 4
- sSup_image2proof · cited by 3
- iSupIndep_def'proof · cited by 3
- SupClosed.biSup_memproof · cited by 3
- exists_sSupIndep_disjoint_sSup_atomsproof · cited by 2