Theorems · Definition · order theory
OrderHom.prevFixed
{α : Type u} → [inst : CompleteLattice α] → (f : α →o α) → (x : α) → f x ≤ x → ↑(Function.fixedPoints ⇑f)Previous fixed point of a monotone map. If f is a monotone self-map of a complete lattice and
x is a point such that f x ≤ x, then f.prevFixed x hx is the greatest fixed point of f
that is less than or equal to x.
- Defined in
- Mathlib.Order.FixedPoints
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Set.Elemstatement · cited by 7,166
- CompleteLatticestatement and proof · cited by 1,048
- OrderHomstatement and proof · cited by 934
- Function.fixedPointsstatement · cited by 90
- OrderHom.gfpproof · cited by 16
- OrderHom.constproof · cited by 8
Cited by5
Results whose statement or proof uses this declaration.
- OrderHom.nextFixedproof · cited by 4
- OrderHom.prevFixed_lestatement · cited by 1
- OrderHom.le_prevFixed_iffstatement · cited by 1
- OrdinalApprox.prevFixed_eq_iInf_gfpApproxstatement · cited by 0
- OrderHom.le_prevFixedstatement · cited by 0