intuition.
unfold lowDistApprox, evalDet_equiv in *.
destruct H0. destruct H0. intuition.
exists x.
exists x0.
intuition.
eapply rel_map_impl.
eapply H1.
intuition.
eapply H.
trivial.
unfold lowDistApprox, evalDet_equiv in *.
destruct H0. destruct H0. intuition.
exists x.
exists x0.
intuition.
eapply rel_map_impl.
eapply H1.
intuition.
eapply H.
trivial.
Qed.

Theorem det_eq_impl_dist_sem_eq : forall (A : Set)(c1 c2 : Comp A),
well_formed_comp c1 ->
well_formed_comp c2 -> (* perhaps we can conclude this from the equivalence? *)
evalDet_equiv c1 c2 ->
dist_sem_eq c1 c2.