Theorems · Theorem · order theory
ciSup_subtype_fun
∀ {α : Type u_1} [inst : ConditionallyCompleteLattice α] {ι : Type u_5} {s : Set ι} {f : ι → α},
BddAbove (Set.range fun i => f ↑i) → sSup ∅ ≤ ⨆ i, f ↑i → ⨆ i, f ↑i = ⨆ t ∈ s, f t- Cited by
- 2 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- ConditionallyCompleteLattice
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.Elemstatement and proof · cited by 7,166
- Set.rangestatement and proof · cited by 4,705
- iSupstatement and proof · cited by 2,415
- SupSet.sSupstatement and proof · cited by 954
- BddAbovestatement and proof · cited by 620
- ConditionallyCompleteLatticestatement and proof · cited by 364
- ciSup_subtypeproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- csSup_imageproof · cited by 3
- ciSup_subtype''proof · cited by 0