Theorems · Theorem · order theory
cbiSup_eq_of_forall_not
∀ {α : Type u_1} {ι : Sort u_4} [inst : ConditionallyCompletePartialOrderSup α] {p : ι → Prop} {f : (i : ι) → p i → α},
(∀ (i : ι), ¬p i) → ⨆ i, ⨆ (h : p i), f i h = sSup ∅- Cited by
- 2 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
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
- iSupstatement and proof · cited by 2,415
- SupSet.sSupstatement and proof · cited by 954
- IsEmptyproof · cited by 759
- isEmpty_or_nonemptyproof · cited by 269
- ConditionallyCompletePartialOrderSupstatement and proof · cited by 52
- ciSup_constproof · cited by 43
- iSup_of_empty'proof · cited by 16
Cited by2
Results whose statement or proof uses this declaration.
- ciSup_subtypeproof · cited by 4
- cbiSup_emptyproof · cited by 1