reserve x for set,
  i,j,k,n for Nat,
  K for Field;
reserve a,b,c,d for Element of K;
reserve D for non empty set;

theorem Th36:
  for f being Permutation of Seg n holds f is FinSequence of Seg n
proof
  let f be Permutation of Seg n;
A1: rng f c= Seg n by RELAT_1:def 19;
  per cases;
  suppose
    n = 0;
    hence thesis by A1,FINSEQ_1:def 4;
  end;
  suppose
    n <> 0;
    then dom f = Seg n by FUNCT_2:def 1;
    then f is FinSequence by FINSEQ_1:def 2;
    hence thesis by A1,FINSEQ_1:def 4;
  end;
end;
