generalize (D_Rs_2 0); intro; rewrite Rs_0 in H; rewrite Ropp_0 in H;
rewrite Rmult_0_l in H;
generalize
(Rmult_integral (derive_pt Rs 0 (Rs_derivable 0%R))
(2 * derive_pt alphas 0 (cond_D1 alphas 0%R) -
derive_pt thetat 0 (thetat_derivable 0%R)) H);
intro H1; elim H1; intro; generalize D_Rs_0_strong;
intro.
rewrite H0 in H2; elim (Rlt_irrefl 0 H2).
generalize
(Rminus_diag_uniq_sym (derive_pt thetat 0 (thetat_derivable 0%R))
(2 * derive_pt alphas 0 (cond_D1 alphas 0%R)) H0);
intro; symmetry  in |- *; assumption.
Qed.

(**********)
Lemma D_Rs_pos_non_null :
forall t : R,
(0 < t)%R ->
(forall x : R, (0 < x < t)%R -> (0 < derive_pt Rs x (Rs_derivable x))%R) ->
(0 < Rs t)%R.