Theorems · Theorem · order theory
sSup_sUnion
∀ {β : Type u_2} [inst : CompleteLattice β] (s : Set (Set β)), sSup (⋃₀ s) = ⨆ t ∈ s, sSup t- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.iUnionproof · cited by 2,483
- iSupstatement and proof · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- SupSet.sSupstatement and proof · cited by 954
- Set.sUnionstatement · cited by 392
- iSup_congr_Propproof · cited by 247
- Set.sUnion_eq_biUnionproof · cited by 51
- sSup_eq_iSupproof · cited by 42
- iSup_iUnionproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- exists_sSupIndep_disjoint_sSup_atomsproof · cited by 2
- sInf_sUnionproof · cited by 0