Theorems · Theorem · order theory
iSup_sUnion
∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLattice β] (S : Set (Set α)) (f : α → β),
⨆ x ∈ ⋃₀ S, f x = ⨆ s ∈ S, ⨆ x ∈ s, f x- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 19 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.
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
- iSupstatement and proof · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- Set.sUnionstatement · cited by 392
- Set.sUnion_eq_iUnionproof · cited by 26
- iSup_subtype''proof · cited by 18
- iSup_iUnionproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- exists_sUnionproof · cited by 0