(* Easy to prove with constructive reals *)
Axiom r_sin_rho : (ConflictRange < r_vi * sin rho_vi)%R.Definition l : R := Die 0 T.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.