reserve k,n,i,j for Nat;

theorem Th27:
  for n being Nat, IT being Element of Permutations(n)
  st n>=1 holds IT is even iff IT" is even
proof
  let n be Nat, IT be Element of Permutations(n);
  assume
A1: n>=1;
  hence IT is even implies IT" is even by Lm2;
  now
    assume IT" is even;
    then IT"" is even by A1,Lm2;
    hence IT is even by FUNCT_1:43;
  end;
  hence thesis;
end;
