reserve A for non empty set,
  a,b,x,y,z,t for Element of A,
  f,g,h for Permutation of A;
reserve R for Relation of [:A,A:];

theorem
  f is_FormalIz_of R & g is_automorphism_of R implies f\g is_FormalIz_of R
proof
  assume that
A1: for x,y holds [[x,y],[f.x,f.y]] in R and
A2: for x,y,z,t holds ([[x,y],[z,t]] in R iff [[g.x,g.y],[g.z,g.t]] in R );
  let x,y;
A3: [[g".x,g".y],[f.(g".x),f.(g".y)]] in R by A1;
  g.(g".x) = x & g.(g".y) = y by Th2;
  then [[x,y],[g.(f.(g".x)),g.(f.(g".y))]] in R by A2,A3;
  then [[x,y],[(g*f).(g".x),g.(f.(g".y))]] in R by FUNCT_2:15;
  then [[x,y],[(g*f).(g".x),(g*f).(g".y)]] in R by FUNCT_2:15;
  then [[x,y],[((g*f)*g").x,(g*f).(g".y)]] in R by FUNCT_2:15;
  hence thesis by FUNCT_2:15;
end;
