Theorems · Theorem · order theory
DirectedOn.ciInf_set_le
∀ {α : Type u_1} {β : Type u_2} [inst : ConditionallyCompletePartialOrderInf α] {f : β → α} {s : Set β},
DirectedOn (fun x1 x2 => x2 ≤ x1) (f '' s) → BddBelow (f '' s) → ∀ {c : β}, c ∈ s → ⨅ i, f ↑i ≤ f c- Cited by
- 0 results in Mathlib
- 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
- iInfstatement · cited by 1,690
- BddBelowstatement and proof · cited by 401
- Set.mem_image_of_memproof · cited by 371
- DirectedOnstatement and proof · cited by 271
- ConditionallyCompletePartialOrderInfstatement and proof · cited by 51
- LE.le.trans_eq'proof · cited by 21
- sInf_image'proof · cited by 9
- DirectedOn.csInf_leproof · cited by 9
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