Theorems · Theorem · logic and foundations
OrdinalApprox.lfpApprox_ord_mem_fixedPoint
∀ {α : Type u} [inst : CompleteLattice α] (f : α →o α) {x : α},
x ≤ f x → OrdinalApprox.lfpApprox f x (Order.succ (Cardinal.mk α)).ord ∈ Function.fixedPoints ⇑fThe approximation at the index of the successor of the domain's cardinality is a fixed point
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Cardinalstatement · cited by 2,598
- LT.lt.leproof · cited by 2,189
- Ordinalproof · cited by 1,688
- CompleteLatticestatement and proof · cited by 1,048
- Cardinal.mkstatement and proof · cited by 942
- OrderHomstatement and proof · cited by 934
- Order.succstatement and proof · cited by 633
- le_totalproof · cited by 294
- Cardinal.ordstatement and proof · cited by 266
- Function.fixedPointsstatement and proof · cited by 90
Cited by3
Results whose statement or proof uses this declaration.
- OrdinalApprox.lfpApprox_ord_eq_lfpproof · cited by 2
- OrdinalApprox.gfpApprox_ord_mem_fixedPointproof · cited by 1
- OrdinalApprox.nextFixed_eq_iSup_lfpApproxproof · cited by 1