Theorems · Theorem · order theory
OrderHom.le_prevFixed
∀ {α : Type u} [inst : CompleteLattice α] (f : α →o α) {x : α} (hx : f x ≤ x) {y : ↑(Function.fixedPoints ⇑f)},
↑y ≤ x → y ≤ f.prevFixed x hx- Defined in
- Mathlib.Order.FixedPoints
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
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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.prevFixedstatement · cited by 4
- OrderHom.le_prevFixed_iffproof · cited by 1
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