unfold u in |- *; unfold derivable in |- *; intro.
reg.
apply yP_derivable.
apply xP_derivable.
apply Rle_lt_trans with (Rsqr (xP x) + Rsqr (yP x))%R.
apply Rplus_le_le_0_compat; apply Rle_0_sqr.
rewrite Rplus_assoc.
apply Rplus_lt_compat_l.
pattern (Rsqr (yP x)) at 1 in |- *; rewrite <- Rplus_0_r.
apply Rplus_lt_compat_l.
apply Rsqr_pos_lt.
red in |- *; intro; assert (H0 := cond_pos eps); rewrite H in H0;
elim (Rlt_irrefl _ H0).
Qed.

(* Specifications: *)
Lemma fct_der2 :
forall (eps : posreal) (t : R), derivable_pt (fun y : R => Rsqr (u eps y)) t.