Theorems · Theorem · dynamical systems
CircleDeg1Lift.le_iterate_of_add_int_le_map
∀ (f : CircleDeg1Lift) {x : ℝ} {m : ℤ}, x + ↑m ≤ f x → ∀ (n : ℕ), x + ↑n * ↑m ≤ (⇑f)^[n] x- Cited by
- 2 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.
Cites12
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
- Function.Commute.symmproof · cited by 9
- CircleDeg1Lift.commute_add_intproof · cited by 9
- Monotone.add_constproof · cited by 7
- Function.Commute.iterate_le_of_map_leproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- CircleDeg1Lift.le_translationNumber_of_add_int_leproof · cited by 4
- CircleDeg1Lift.mul_floor_map_zero_le_floor_iterate_zeroproof · cited by 0