Theorems · Theorem · order theory
Directed.le_ciSup_of_le
∀ {α : Type u_1} {ι : Sort u_4} [inst : ConditionallyCompletePartialOrderSup α] {a : α} {f : ι → α},
Directed (fun x1 x2 => x1 ≤ x2) f → BddAbove (Set.range f) → ∀ (c : ι), a ≤ f c → a ≤ iSup f- Cited by
- 1 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.rangestatement and proof · cited by 4,705
- iSupstatement · cited by 2,415
- le_transproof · cited by 985
- BddAbovestatement and proof · cited by 620
- Directedstatement and proof · cited by 213
- ConditionallyCompletePartialOrderSupstatement and proof · cited by 52
- Directed.le_ciSupproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Directed.ciSup_monoproof · cited by 0