Theorems · Theorem · order theory
DirectedOn.le_csSup
∀ {α : Type u_2} [inst : ConditionallyCompletePartialOrderSup α] {s : Set α} {a : α},
DirectedOn (fun x1 x2 => x1 ≤ x2) s → BddAbove s → a ∈ s → a ≤ sSup s- Cited by
- 9 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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 · cited by 954
- BddAbovestatement and proof · cited by 620
- DirectedOnstatement and proof · cited by 271
- ConditionallyCompletePartialOrderSupstatement and proof · cited by 52
- DirectedOn.isLUB_csSupproof · cited by 9
Cited by9
Results whose statement or proof uses this declaration.
- Directed.le_ciSupproof · cited by 4
- DirectedOn.csSup_eq_of_forall_le_of_forall_lt_exists_gtproof · cited by 1
- DirectedOn.notMem_of_csSup_ltproof · cited by 0
- DirectedOn.subset_Icc_csInf_csSupproof · cited by 0
- DirectedOn.le_ciSup_setproof · cited by 0
- DirectedOn.le_csSup_iffproof · cited by 0
- DirectedOn.le_csSup_of_leproof · cited by 0
- DirectedOn.lt_csSup_of_ltproof · cited by 0
- DirectedOn.csSup_le_csSupproof · cited by 0