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

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.