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Theorems · Theorem · order theory

OrderHom.nextFixed_le_iff

∀ {α : Type u} [inst : CompleteLattice α] (f : α →o α) {x : α} (hx : x ≤ f x) {y : ↑(Function.fixedPoints ⇑f)},
  f.nextFixed x hx ≤ y ↔ x ≤ ↑y
Defined in
Mathlib.Order.FixedPoints
Cited by
1 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Quot.sound
Assumes
CompleteLattice
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

OrderHom.le_prevFixed_iff · cited by 1OrderHom.le_prevFixed_iffDFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetSet.Elem · cited by 7166Set.ElemLE.le.trans · cited by 3151le.transCompleteLattice · cited by 1048CompleteLatticeOrderHom · cited by 934OrderHomFunction.fixedPoints · cited by 90Function.fixedPointsOrderHom.nextFixed · cited by 4OrderHom.nextFixedOrderHom.nextFixed_le · cited by 2OrderHom.nextFixed_leOrderHom.le_nextFixed · cited by 2OrderHom.le_nextFixedOrderHom.nextFixed_le_iffCITED BYCITES

Cites10

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Cited by1

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