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
  for a being Element of Group_of_Perm 3 st a = <*2,3,1*> holds a" = <*3 ,1,2*>
proof
  let a be Element of Group_of_Perm 3;
  reconsider a1 = a as Element of Permutations 3 by MATRIX_1:def 13;
  assume a = <*2,3,1*>;
  then a1" = <*3,1,2*> by Th28;
  hence thesis by MATRIX_7:27;
end;
