unfold trkrate in |- *; replace (r (mkBank 0 cond1_0 cond2_0)) with 0%R...
unfold toDeg, tand in |- *; unfold toRad in |- *; repeat rewrite Rmult_0_l;
rewrite tan_0; unfold Rdiv in |- *; repeat rewrite Rmult_assoc;
repeat rewrite Rmult_0_l; apply Rmult_0_r...
Qed.
Definition distance (s1 s2 : State) : R :=
sqrt (Rsqr (xt s2 - xt s1) + Rsqr (yt s2 - yt s1)).

Lemma distance_sym : forall s1 s2 : State, distance s1 s2 = distance s2 s1.
Proof with trivial.