Theorems · Theorem · order theory
Monotone.antitone_iterate_of_map_le
∀ {α : Type u_1} [inst : Preorder α] {f : α → α} {x : α}, Monotone f → f x ≤ x → Antitone fun n => f^[n] xIf f is a monotone map and f x ≤ x at some point x, then the iterates f^[n] x form
an antitone sequence.
- Defined in
- Mathlib.Order.Iterate
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
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
- Monotonestatement and proof · cited by 1,397
- Nat.iteratestatement · cited by 740
- Antitonestatement · cited by 563
- Monotone.dualproof · cited by 39
- Monotone.monotone_iterate_of_le_mapproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- toZ_strictMonoproof · cited by 3