Theorems · Theorem · order theory
Directed.le_ciSup
∀ {ι : Sort u_1} {α : Type u_2} [inst : ConditionallyCompletePartialOrderSup α] {f : ι → α},
Directed (fun x1 x2 => x1 ≤ x2) f → BddAbove (Set.range f) → ∀ (i : ι), f i ≤ ⨆ j, f j- Cited by
- 4 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
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.
- Set.rangestatement and proof · cited by 4,705
- iSupstatement · cited by 2,415
- BddAbovestatement and proof · cited by 620
- Set.mem_range_selfproof · cited by 328
- Directedstatement and proof · cited by 213
- ConditionallyCompletePartialOrderSupstatement and proof · cited by 52
- Directed.directedOn_rangeproof · cited by 17
- DirectedOn.le_csSupproof · cited by 9
Cited by4
Results whose statement or proof uses this declaration.
- Directed.le_ciSup_of_leproof · cited by 1
- ciSup_Iicproof · cited by 1
- Monotone.ciSup_mem_iInter_Icc_of_antitoneproof · cited by 1
- Directed.ciInf_le_ciSupproof · cited by 0