Theorems · Theorem · dynamical systems
CircleDeg1Lift.iterate_le_of_map_le_add_int
∀ (f : CircleDeg1Lift) {x : ℝ} {m : ℤ}, f x ≤ x + ↑m → ∀ (n : ℕ), (⇑f)^[n] x ≤ x + ↑n * ↑m- Cited by
- 1 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Nat.iteratestatement and proof · cited by 740
- nsmul_eq_mulproof · cited by 369
- CircleDeg1Liftstatement and proof · cited by 128
- monotone_idproof · cited by 31
- add_right_iterateproof · cited by 11
- CircleDeg1Lift.monotoneproof · cited by 11
- CircleDeg1Lift.commute_add_intproof · cited by 9
- Monotone.add_constproof · cited by 7
- Function.Commute.iterate_le_of_map_leproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- CircleDeg1Lift.translationNumber_le_of_le_add_intproof · cited by 4