Theorems · Theorem · order theory
iSup_image
∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLattice α] {γ : Type u_8} {f : β → γ} {g : γ → α} {t : Set β},
⨆ c ∈ f '' t, g c = ⨆ b ∈ t, g (f b)- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.imagestatement and proof · cited by 5,609
- iSupstatement and proof · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- SupSet.sSupproof · cited by 954
- Set.image_compproof · cited by 142
- sSup_imageproof · cited by 36
Cited by12
Results whose statement or proof uses this declaration.
- Set.biUnion_imageproof · cited by 17
- TopologicalSpace.Opens.isBasis_iff_coverproof · cited by 4
- Ideal.smul_restrictScalarsproof · cited by 3
- Metric.hausdorffEDist_imageproof · cited by 2
- Function.frameMinimalAxiomsproof · cited by 2
- Topology.IsInducing.nhdsSet_eq_comapproof · cited by 2
- Set.BijOn.iSup_compproof · cited by 2
- Submodule.fg_iff_compactproof · cited by 1
- Finset.iSup_finset_imageproof · cited by 1
- disjoint_biSup_of_finite_disjoint_biSupproof · cited by 1
- iSup_image2proof · cited by 1
- PointedCone.ofSubmodule_iSupproof · cited by 0