Theorems · Theorem · order theory
exists_pred_iterate_iff_le
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : PredOrder α] [IsPredArchimedean α] {a b : α},
(∃ n, Order.pred^[n] a = b) ↔ b ≤ a- Defined in
- Mathlib.Order.SuccPred.Archimedean
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
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Cites8
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 and proof · cited by 740
- PredOrderstatement and proof · cited by 334
- Order.predstatement and proof · cited by 273
- IsPredArchimedeanstatement and proof · cited by 66
- Order.pred_leproof · cited by 19
- IsPredArchimedean.exists_pred_iterate_of_leproof · cited by 11
- Function.iterate_le_id_of_le_idproof · cited by 3
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