Theorems · Theorem · order theory
cbiSup_eq_ciSup_subtype
∀ {α : Type u_1} {ι : Sort u_4} [inst : ConditionallyCompleteLattice α] {p : ι → Prop} {f : (i : ι) → p i → α},
BddAbove (Set.range fun i => f ↑i ⋯) → sSup ∅ ≤ ⨆ i, f ↑i ⋯ → ⨆ i, ⨆ (h : p i), f i h = ⨆ x, f ↑x ⋯- Cited by
- 1 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 · cited by 53,352
- 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
- Subtype.propstatement and proof · cited by 505
- ConditionallyCompleteLatticestatement and proof · cited by 364
- ciSup_subtypeproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- ciSup_subtype'proof · cited by 0