Theorems · Theorem · order theory
Order.le_succ_iterate
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : SuccOrder α] (k : ℕ) (x : α), x ≤ Order.succ^[k] x- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
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
- Order.succstatement · cited by 633
- SuccOrderstatement and proof · cited by 574
- Order.le_succproof · cited by 96
- Function.id_le_iterate_of_id_leproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- strictMonoOn_of_lt_succproof · cited by 4
- monotoneOn_of_le_succproof · cited by 3
- toZ_iterate_succ_of_not_isMaxproof · cited by 1
- le_total_of_codirectedproof · cited by 1
- toZ_iterate_succ_leproof · cited by 0