set X = PrefSpace {};
the ToleranceRel of (PrefSpace {}) /\ the InternalRel of (PrefSpace {}) = {} ;
then the PrefRel of (PrefSpace {}), the ToleranceRel of (PrefSpace {}), the InternalRel of (PrefSpace {}) are_mutually_disjoint by XBOOLE_0:def 7;
hence ( PrefSpace {} is empty & PrefSpace {} is preference-like ) ; :: thesis: verum