Theorems · Theorem · order theory
cbiSup_eq_of_not_forall
∀ {α : Type u_1} {ι : Sort u_4} [inst : ConditionallyCompleteLinearOrder α] {p : ι → Prop} {f : Subtype p → α},
(¬∀ (i : ι), p i) → ⨆ i, ⨆ (h : p i), f ⟨i, h⟩ = max (iSup f) (sSup ∅)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.rangeproof · cited by 4,705
- LE.le.transproof · cited by 3,151
- iSupstatement and proof · cited by 2,415
- LT.lt.leproof · cited by 2,189
- SupSet.sSupstatement and proof · cited by 954
- LT.lt.neproof · cited by 872
- BddAboveproof · cited by 620
- Eq.leproof · cited by 605
- ConditionallyCompleteLinearOrderstatement and proof · cited by 542
- le_or_gtproof · cited by 269
- Eq.trans_leproof · cited by 155
Cited by2
Results whose statement or proof uses this declaration.
- Measurable.biSupproof · cited by 3
- cbiInf_eq_of_not_forallproof · cited by 0