Definition e (t : R) : R := sqrt (Rsqr_evader_distance t).Definition i (t : R) : R := sqrt (Rsqr_intruder_distance t).

(* Specifications: *)
Lemma conflict_T_e_0 : conflict T = true -> (e T <= ConflictRange)%R.
Lemma conflict_T_e_1 : (e T <= ConflictRange)%R -> conflict T = true.
Lemma L : Rsqr l = (Rsqr (xe - xi intr 0) + Rsqr (ye - yi intr 0))%R.
Lemma L_intruder : forall t : R, (l <= e t + i t)%R.
Lemma l_is_pos : (0 <= l)%R.
Lemma L_e : forall t : R, (e t <= l + i t)%R.
Lemma L_i : forall t : R, (i t <= l + e t)%R.
Lemma theta_inv : forall t : R, (0 <= t)%R -> (thetat intr 0 - rho_vi * t <= thetat intr t)%R /\ (thetat intr t <= thetat intr 0 + rho_vi * t)%R.
Lemma rho_t_pos : forall t : R, (0 <= t)%R -> (0 <= rho_vi * t)%R.
Lemma rho_t_le : forall t1 t2 : R, (t1 <= t2)%R -> (rho_vi * t1 <= rho_vi * t2)%R.
Lemma Dyp : forall t : R, derive_pt yp t (yp_derivable t) = (v (vi intr) * sin (thetat intr t - thetat intr 0))%R.
Lemma Dyp0_PI2 : forall t : R, (0 <= t)%R -> (rho_vi * t <= PI / 2)%R -> (- (vi intr * sin (rho_vi * t)) <= derive_pt yp t (yp_derivable t) <= vi intr * sin (rho_vi * t))%R.
Lemma yp0 : yp 0 = (l * sin (thetat intr 0 + beta))%R.