(** Composition by linear functions *)

(* Specifications: *)
Lemma is_lim_comp_lin (f : R -> R) (a b : R) (x l : Rbar) :
is_lim f (Rbar_plus (Rbar_mult a x) b) l -> a <> 0
-> is_lim (fun y => f (a * y + b)) x l.
Lemma ex_lim_comp_lin (f : R -> R) (a b : R) (x : Rbar) :
ex_lim f (Rbar_plus (Rbar_mult a x) b)
-> ex_lim (fun y => f (a * y + b)) x.
Lemma Lim_comp_lin (f : R -> R) (a b : R) (x : Rbar) :
ex_lim f (Rbar_plus (Rbar_mult a x) b) -> a <> 0 ->
Lim (fun y => f (a * y + b)) x = Lim f (Rbar_plus (Rbar_mult a x) b).