Theorems · Theorem · order theory
DirectedOn.csSup_le_iff
∀ {α : Type u_1} [inst : ConditionallyCompletePartialOrderSup α] {s : Set α} {a : α},
DirectedOn (fun x1 x2 => x1 ≤ x2) s → BddAbove s → s.Nonempty → (sSup s ≤ a ↔ ∀ b ∈ s, b ≤ a)- Cited by
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- Foundations
- Depth 9 from the axioms · uses propext, Quot.sound
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- 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
- isLUB_le_iffproof · cited by 24
- DirectedOn.isLUB_csSupproof · cited by 9
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