apply Rmult_lt_0_compat; [ prove_sup | apply Rinv_0_lt_compat; prove_sup ].
Qed.

(**********)
Lemma Math_prop_y_a_PI2 :
forall (a l : R) (T : TimeT),
(MinBeta <= a)%R ->
(a <= PI / 2)%R ->
(0 <= l)%R ->
(l * sin MinBeta + r_V * (cos (rho_V * T) - 1) <=
l * sin a + r_V * (cos (rho_V * T) - 1))%R.