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

Lemma maj_term1 : forall (x h eps l1 alp_f2:R) (eps_f2 alp_f1d:posreal) (f1 f2:R -> R), 0 < eps -> f2 x <> 0 -> f2 (x + h) <> 0 -> (forall h:R, h <> 0 -> Rabs h < alp_f1d -> Rabs ((f1 (x + h) - f1 x) / h - l1) < Rabs (eps * f2 x / 8)) -> (forall a:R, Rabs a < Rmin eps_f2 alp_f2 -> / Rabs (f2 (x + a)) < 2 / Rabs (f2 x)) -> h <> 0 -> Rabs h < alp_f1d -> Rabs h < Rmin eps_f2 alp_f2 -> Rabs (/ f2 (x + h) * ((f1 (x + h) - f1 x) / h - l1)) < eps / 4.