Theorems · Theorem · order theory
Order.pred_iterate_le
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : PredOrder α] (k : ℕ) (x : α), Order.pred^[k] x ≤ x- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 6 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
- PredOrderstatement and proof · cited by 334
- Order.predstatement · cited by 273
- Order.pred_leproof · cited by 19
- Function.iterate_le_id_of_le_idproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- strictMonoOn_of_pred_ltproof · cited by 3
- monotoneOn_of_pred_leproof · cited by 3
- le_total_of_directedproof · cited by 2
- toZ_iterate_pred_of_not_isMinproof · cited by 1
- toZ_iterate_pred_geproof · cited by 0
- IsPredArchimedean.findAtom_leproof · cited by 0