Theorems · Theorem · order theory
DirectedOn.le_ciSup_set
∀ {α : Type u_1} {β : Type u_2} [inst : ConditionallyCompletePartialOrderSup α] {f : β → α} {s : Set β},
DirectedOn (fun x1 x2 => x1 ≤ x2) (f '' s) → BddAbove (f '' s) → ∀ {c : β}, c ∈ s → f c ≤ ⨆ i, f ↑i- Cited by
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- Foundations
- Depth 10 from the axioms · uses propext, Quot.sound
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Cites11
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.Elemstatement · cited by 7,166
- Set.imagestatement and proof · cited by 5,609
- iSupstatement · cited by 2,415
- BddAbovestatement and proof · cited by 620
- Set.mem_image_of_memproof · cited by 371
- LE.le.trans_eqproof · cited by 328
- DirectedOnstatement and proof · cited by 271
- ConditionallyCompletePartialOrderSupstatement and proof · cited by 52
- sSup_image'proof · cited by 10
- DirectedOn.le_csSupproof · cited by 9
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