(* begin hide *)
Notation Rmin_pos := Rmin_pos (only parsing). (* compat *)
(* end hide *)

Lemma maj_term3 :
forall (x h eps l2 alp_f2:R) (eps_f2 alp_f2d:posreal)
(f1 f2:R -> R),
0 < eps ->
f2 x <> 0 ->
f2 (x + h) <> 0 ->
(forall h:R,
h <> 0 ->
Rabs h < alp_f2d ->
Rabs ((f2 (x + h) - f2 x) / h - l2) <
Rabs (Rsqr (f2 x) * eps / (8 * f1 x))) ->
(forall a:R,
Rabs a < Rmin eps_f2 alp_f2 -> / Rabs (f2 (x + a)) < 2 / Rabs (f2 x)) ->
h <> 0 ->
Rabs h < alp_f2d ->
Rabs h < Rmin eps_f2 alp_f2 ->
f1 x <> 0 ->
Rabs (f1 x / (f2 x * f2 (x + h)) * ((f2 (x + h) - f2 x) / h - l2)) <
eps / 4.