intros; generalize (xpt t H H0); intro; unfold Rminus, hx in H1;
rewrite xp0 in H1;
generalize
(Rplus_le_compat_l (- l * cos (thetat intr 0 + beta))
(r_vi * sin (rho_vi * t)) (xp t + - (- l * cos (thetat intr 0 + beta)))
H1); rewrite <- (Rplus_comm (r_vi * sin (rho_vi * t)));
rewrite (Rplus_comm (- l * cos (thetat intr 0 + beta)));
repeat rewrite Rplus_assoc; rewrite Rplus_opp_l; rewrite Rplus_0_r;
rewrite (Rplus_comm beta); unfold Rminus in |- *;
intro;
replace (- (l * cos (thetat intr 0 + beta)))%R with
(- l * cos (thetat intr 0 + beta))%R; [ assumption | ring ].
Qed.

Lemma Omega_defeq :
forall x : R, Omega x = true -> (PI / 2 <= x <= 3 * (PI / 2))%R.