Theorems · Theorem · order theory
OrderHom.le_map_sup_fixedPoints
∀ {α : Type u} [inst : CompleteLattice α] (f : α →o α) (x y : ↑(Function.fixedPoints ⇑f)), ↑x ⊔ ↑y ≤ f (↑x ⊔ ↑y)- Defined in
- Mathlib.Order.FixedPoints
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses no axioms
- Assumes
- CompleteLattice
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.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Set.Elemstatement and proof · cited by 7,166
- CompleteLatticestatement and proof · cited by 1,048
- OrderHomstatement and proof · cited by 934
- Function.fixedPointsstatement and proof · cited by 90
- OrderHom.monoproof · cited by 28
- Monotone.le_map_supproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- OrderHom.map_inf_fixedPoints_leproof · cited by 0