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 derive_pt_mirr :
forall f (x:R) (pr1:derivable_pt f (-x)),
derive_pt (mirr_fct f) x (derivable_pt_mirr _ _ pr1) = - derive_pt f (-x) pr1.