Theorems · Theorem · order theory
Monotone.iterate
∀ {α : Type u} [inst : Preorder α] {f : α → α}, Monotone f → ∀ (n : ℕ), Monotone f^[n]- Defined in
- Mathlib.Order.Monotone.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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 and proof · cited by 740
- Monotone.compproof · cited by 67
- monotone_idproof · cited by 31
Cited by3
Results whose statement or proof uses this declaration.
- Monotone.monotone_iterate_of_le_mapproof · cited by 3
- Function.Commute.iterate_le_of_map_leproof · cited by 2
- OrderHom.iterate_sup_le_sup_iffproof · cited by 1