Theorems · Theorem · order theory
DirectedOn.csSup_le_csSup
∀ {α : Type u_1} [inst : ConditionallyCompletePartialOrderSup α] {s t : Set α},
DirectedOn (fun x1 x2 => x1 ≤ x2) s →
DirectedOn (fun x1 x2 => x1 ≤ x2) t → BddAbove t → s.Nonempty → s ⊆ t → sSup s ≤ sSup t- Cited by
- 0 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.Nonemptystatement and proof · cited by 2,627
- SupSet.sSupstatement · cited by 954
- BddAbovestatement and proof · cited by 620
- DirectedOnstatement and proof · cited by 271
- ConditionallyCompletePartialOrderSupstatement and proof · cited by 52
- DirectedOn.le_csSupproof · cited by 9
- DirectedOn.csSup_leproof · cited by 4
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