set P = PIStr(# {{}},({} ({{}},{{}})),(id {{}}) #);
reconsider P = PIStr(# {{}},({} ({{}},{{}})),(id {{}}) #) as non empty strict PIStr ;
take P ; :: thesis: P is PI-preference-like
AB: the ToleranceRel of P = {[{},{}]} by SYSREL:13;
the PrefRel of P \/ ( the PrefRel of P ~) = {} ;
hence P is PI-preference-like by ZFMISC_1:29, AB; :: thesis: verum