theorem Th9:
  u in Lex(E) iff len u = 1
proof
  thus u in Lex(E) implies len u = 1
  proof
    assume u in Lex(E);
    then ex e st e in E & u = <%e%> by FLANG_1:def 4;
    hence thesis by AFINSQ_1:def 4;
  end;
  assume len u = 1;
  then ex e st <%e%> = u & e = u.0 by Th4;
  hence thesis by FLANG_1:def 4;
end;
