unfold beta in |- *; case beta_exists; trivial.
Qed.
Definition Omega (a : R) : bool :=
match Rle_dec (PI / 2) a with
| left _ =>
match Rle_dec a (3 * (PI / 2)) with
| left _ => true
| right _ => false
end
| right _ => false
end.

(* Specifications: *)
Lemma xe_0 : xe = (l * cos beta + xi intr 0)%R.
Proof with trivial.