Theorems · Theorem · order theory
cbiSup_of_not_bddAbove
∀ {α : Type u_1} {ι : Sort u_4} [inst : ConditionallyCompleteLinearOrder α] {p : ι → Prop} {f : (i : ι) → p i → α},
¬BddAbove (Set.range fun i => f ↑i ⋯) → ⨆ i, ⨆ (h : p i), f i h = sSup ∅- Cited by
- 1 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
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 · cited by 53,352
- Set.rangestatement and proof · cited by 4,705
- iSupstatement and proof · cited by 2,415
- SupSet.sSupstatement · cited by 954
- BddAbovestatement and proof · cited by 620
- ConditionallyCompleteLinearOrderstatement and proof · cited by 542
- Subtype.propstatement and proof · cited by 505
- upperBoundsproof · cited by 263
- ciSup_of_not_bddAboveproof · cited by 9
- ciSup_posproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- cbiSup_eq_of_not_forallproof · cited by 2