theorem
  f is negative_dilatation implies f" is negative_dilatation
proof
  assume
A1: f is negative_dilatation;
  let x,y;
  set x9=f".x, y9=f".y;
  f.x9=x & f.y9=y by Th2;
  then y9,x9 // x,y by A1;
  hence thesis by DIRAF:2;
end;
