theorem Th9:
  1 < len (fin^<*b*>^<*c*>)
proof
  len (fin^<*b*>^<*c*>) = len (fin^<*b*>) + len <*c*> by FINSEQ_1:22;
  then len (fin^<*b*>^<*c*>) = len (fin^<*b*>) + 1 by FINSEQ_1:39;
  then len (fin^<*b*>^<*c*>) = len fin + len <*b*> + 1 by FINSEQ_1:22;
  then len (fin^<*b*>^<*c*>) = (len fin + 1) + 1 by FINSEQ_1:39;
  then len (fin^<*b*>^<*c*>) = len fin + (1 + 1);
  then 1 + 1 <= len (fin^<*b*>^<*c*>) by NAT_1:11;
  hence thesis by NAT_1:13;
end;
