Theorems · Theorem · order theory
Relation.fibration_iff_isLowerSet_image_Iic
∀ {α : Type u_1} {β : Type u_2} {f : α → β} [inst : Preorder α] [inst_1 : LE β],
Relation.Fibration (fun x1 x2 => x1 ≤ x2) (fun x1 x2 => x1 ≤ x2) f ↔ ∀ (x : α), IsLowerSet (f '' Set.Iic x)- Defined in
- Mathlib.Order.UpperLower.Fibration
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
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.
- Preorderstatement and proof · cited by 7,952
- Set.imagestatement and proof · cited by 5,609
- le_rflproof · cited by 1,558
- Set.Iicstatement and proof · cited by 1,111
- IsLowerSetstatement and proof · cited by 167
- Relation.Fibrationstatement and proof · cited by 14
- isLowerSet_Iicproof · cited by 8
- IsLowerSet.image_fibrationproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- specializingMap_iff_stableUnderSpecialization_image_singletonproof · cited by 2
- Relation.fibration_iff_image_Iicproof · cited by 2
- Relation.fibration_iff_isLowerSet_imageproof · cited by 2
- Relation.fibration_iff_isUpperSet_image_Iciproof · cited by 0