Theorems · Theorem · order theory
exists_succ_iterate_iff_le
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : SuccOrder α] [IsSuccArchimedean α] {a b : α},
(∃ n, Order.succ^[n] a = b) ↔ a ≤ b- 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
- Order.succstatement and proof · cited by 633
- SuccOrderstatement and proof · cited by 574
- Order.le_succproof · cited by 96
- IsSuccArchimedeanstatement and proof · cited by 88
- IsSuccArchimedean.exists_succ_iterate_of_leproof · cited by 12
- Function.id_le_iterate_of_id_leproof · cited by 4
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