Definition d : R := Die 0 0.
Axiom
beta_exists :
{ beta : R |
xe = (l * cos beta + xi intr 0)%R /\
ye = (yi intr 0 - l * sin beta)%R /\
(0 <= beta + thetat intr 0 < 2 * PI)%R }.
Definition beta := let (a,_) := beta_exists in a.

Lemma beta_def :
xe = (l * cos beta + xi intr 0)%R /\
ye = (yi intr 0 - l * sin beta)%R /\ (0 <= beta + thetat intr 0 < 2 * PI)%R.