Qed.

(**********)
Lemma rho_lb_0 : forall h : TypeSpeed, (rho_lb h < rho h)%R.
intros; unfold rho, rho_lb in |- *; apply Rmult_lt_compat_l;
[ apply g_pos
| generalize TypeSpeed_pos; intros; generalize (H h); clear H; intro H;
generalize (Rinv_0_lt_compat h H); intro H1; generalize tan_MaxBank_lb;
intro H2;
generalize (Rmult_lt_compat_l (/ h) tan_lb_MaxBank (tan MaxBank) H1 H2);
rewrite <- (Rmult_comm (tan MaxBank));
rewrite <- (Rmult_comm tan_lb_MaxBank); intro H3;
assumption ].