Theorems · Theorem · order theory
DirectedOn.isGLB_ciInf_set
∀ {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) → s.Nonempty → IsGLB (f '' s) (⨅ i, f ↑i)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Set.Nonemptystatement and proof · cited by 2,627
- iInfstatement · cited by 1,690
- BddBelowstatement and proof · cited by 401
- DirectedOnstatement and proof · cited by 271
- IsGLBstatement and proof · cited by 213
- Set.Nonempty.imageproof · cited by 87
- ConditionallyCompletePartialOrderInfstatement and proof · cited by 51
- sInf_image'proof · cited by 9
- DirectedOn.isGLB_csInfproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- DirectedOn.le_ciInf_set_iffproof · cited by 0