Theorems · Theorem · order theory
DirectedOn.isLUB_csSup
∀ {α : Type u_2} [inst : ConditionallyCompletePartialOrderSup α] {s : Set α},
DirectedOn (fun x1 x2 => x1 ≤ x2) s → s.Nonempty → BddAbove s → IsLUB s (sSup s)- Cited by
- 9 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- IsLUBstatement · cited by 280
- DirectedOnstatement and proof · cited by 271
- ConditionallyCompletePartialOrderSupstatement and proof · cited by 52
- ConditionallyCompletePartialOrderSup.isLUB_csSup_of_directedproof · cited by 1
Cited by9
Results whose statement or proof uses this declaration.
- tendsto_atTop_ciSupproof · cited by 13
- IsGreatest.csSup_eqproof · cited by 9
- DirectedOn.le_csSupproof · cited by 9
- DirectedOn.csSup_leproof · cited by 4
- GaloisConnection.l_csSup_of_directedOn'proof · cited by 2
- DirectedOn.isLUB_ciSup_setproof · cited by 1
- Directed.isLUB_ciSupproof · cited by 1
- DirectedOn.csInf_le_csSupproof · cited by 0
- DirectedOn.csSup_le_iffproof · cited by 0