theorem Th6:
  len fin <= len (fin^fin1) & len fin1 <= len (fin^fin1) & (fin <>
  {} implies 1 <= len fin & len fin1 < len (fin1^fin))
proof
  len (fin^fin1) = len fin + len fin1 by FINSEQ_1:22;
  hence len fin <= len (fin^fin1) & len fin1 <= len (fin^fin1) by NAT_1:12;
  assume fin <> {};
  then
A1: 0+1 <= len fin by NAT_1:13;
  then len fin1 + 1 <= len fin + len fin1 by XREAL_1:6;
  then len fin1 + 1 <= len (fin1^fin) by FINSEQ_1:22;
  hence thesis by A1,NAT_1:13;
end;
