Theorems · Theorem · order theory
sSup_iUnion
∀ {β : Type u_2} {ι : Sort u_5} [inst : CompleteLattice β] (t : ι → Set β), sSup (⋃ i, t i) = ⨆ i, sSup (t i)- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 2 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.
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.iUnionstatement · cited by 2,483
- iSupstatement and proof · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- SupSet.sSupstatement · cited by 954
- sSup_eq_iSupproof · cited by 42
- iSup_iUnionproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- nhdsSet_iUnionproof · cited by 10
- complementedLattice_of_complementedLattice_Iicproof · cited by 1