theorem Th7:
  len u > 0 implies ex e, u1 st u = <%e%>^u1
proof
  assume len u > 0;
  then consider k such that
A1: len u = k + 1 by NAT_1:6;
  ex u1, e st len u1 = k & u = <%e%>^u1 by A1,FLANG_1:9;
  hence thesis;
end;
