intros f x l a df;
apply (derivable_pt_lim_ext (fun y => a * f y)).
- intros z; rewrite Rmult_comm; reflexivity.
- unfold Rdiv; rewrite Rmult_comm; apply derivable_pt_lim_scal; assumption.
Qed.

Lemma derivable_pt_mirr_prem:
forall (f : R -> R) (x : R), derivable_pt (mirr_fct f) x -> derivable_pt f (-x).