theorem Th30:
  _bool TS is non empty transition-system over Lex(E) \/ {<%>E}
proof
  Lex(E) c= Lex(E) \/ {<%>E} by XBOOLE_1:7;
  then dom the Tran of _bool TS c= [: the carrier of _bool TS, Lex(E) :] & [:
  the carrier of _bool TS, Lex(E) :] c= [: the carrier of _bool TS, Lex(E) \/ {
  <%>E} :] by ZFMISC_1:95;
  hence thesis by RELSET_1:5,XBOOLE_1:1;
end;
