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 Th17:
  f is_automorphism_of R implies f" is_automorphism_of R
proof
  assume
A1: for x,y,z,t holds ([[x,y],[z,t]] in R iff [[f.x,f.y],[f.z,f.t]] in R );
  let x,y,z,t;
A2: f.(f".z) = z & f.(f".t) = t by Th2;
  f.(f".x) = x & f.(f".y) = y by Th2;
  hence thesis by A1,A2;
end;
