theorem Th9:
  len Permutations(n)=n
proof
  set x = the Element of Permutations(n);
  reconsider q=x as Permutation of Seg n by Def12;
A1: dom q=Seg n by FUNCT_2:52;
  then reconsider q as FinSequence by FINSEQ_1:def 2;
  n in NAT by ORDINAL1:def 12;
  then len q=n by A1,FINSEQ_1:def 3;
  hence thesis by Def11;
end;
