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 Th33:
  for p being Permutation of Seg n st p = id Seg n holds not p is
  being_transposition
proof
  let p be Permutation of Seg n;
  assume
A1: p = id Seg n;
  then dom p = Seg n by FUNCT_1:17;
  then
  not ex i,j st i in dom p & j in dom p & i <> j & p.i = j & p.j = i & for
  k st k <> i & k <> j & k in dom p holds p.k = k by A1,FUNCT_1:17;
  hence thesis by MATRIX_1:def 14;
end;
