prove_sup.
rewrite Rmult_0_r; rewrite <- Rmult_comm; rewrite Rmult_assoc;
rewrite <- Rinv_l_sym; [ prove_sup | discrR ].
Qed.

(* Specifications: *)
(**********)
Lemma rho_ub_0 : forall h : TypeSpeed, (rho h < rho_ub h)%R.
intros; unfold rho, rho_ub 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_ub;
intro H2;
generalize (Rmult_lt_compat_l (/ h) (tan MaxBank) tan_ub_MaxBank H1 H2);
rewrite Rmult_comm; rewrite <- (Rmult_comm tan_ub_MaxBank);
intro H3; assumption ].
(**********)
Lemma tan_ub_MaxBank_pos : (0 < tan_ub_MaxBank)%R.
apply Rlt_trans with tan_lb_MaxBank;
[ apply tan_lb_MaxBank_pos
| apply Rlt_trans with (tan MaxBank);
[ apply tan_MaxBank_lb | apply tan_MaxBank_ub ] ].