Theorems · Theorem · order theory
LE.le.exists_pred_iterate
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : PredOrder α] [IsPredArchimedean α] {a b : α},
b ≤ a → ∃ n, Order.pred^[n] a = b- Defined in
- Mathlib.Order.SuccPred.Archimedean
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- Nat.iteratestatement · cited by 740
- PredOrderstatement and proof · cited by 334
- Order.predstatement · cited by 273
- IsPredArchimedeanstatement and proof · cited by 66
- IsPredArchimedean.exists_pred_iterate_of_leproof · cited by 11
Cited by6
Results whose statement or proof uses this declaration.
- Pred.recproof · cited by 4
- Order.IsPredPrelimit.isMax_of_noMinproof · cited by 2
- le_total_of_directedproof · cited by 2
- IsPredArchimedean.findAtom_eq_botproof · cited by 1
- IsPredArchimedean.pred_findAtomproof · cited by 1
- Pred.rec_iffproof · cited by 1