Theorems · Theorem · order theory
DirectedOn.notMem_of_csSup_lt
∀ {α : Type u_1} [inst : ConditionallyCompletePartialOrderSup α] {x : α} {s : Set α},
DirectedOn (fun x1 x2 => x1 ≤ x2) s → sSup s < x → BddAbove s → x ∉ s- 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
- SupSet.sSupstatement and proof · cited by 954
- LE.le.trans_ltproof · cited by 795
- BddAbovestatement and proof · cited by 620
- DirectedOnstatement and proof · cited by 271
- lt_irreflproof · cited by 190
- ConditionallyCompletePartialOrderSupstatement and proof · cited by 52
- DirectedOn.le_csSupproof · cited by 9
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