Theorems · Theorem · order theory
cbiSup_empty
∀ {α : Type u_1} {β : Type u_2} [inst : ConditionallyCompletePartialOrderSup α] {f : β → α}, ⨆ i ∈ ∅, f i = sSup ∅- Cited by
- 1 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- iSupstatement · cited by 2,415
- SupSet.sSupstatement · cited by 954
- ConditionallyCompletePartialOrderSupstatement and proof · cited by 52
- Set.notMem_emptyproof · cited by 35
- cbiSup_eq_of_forall_notproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- ciSup_imageproof · cited by 1