theorem Th70:
  f is dilatation implies f" is dilatation
proof
  assume
A1: f is dilatation;
  now
    let x,y;
    set x9=f".x;
    set y9=f".y;
    f.x9=x & f.y9=y by Th2;
    then x9,y9 // x,y by A1,Th68;
    hence x,y // f".x,f".y by AFF_1:4;
  end;
  hence thesis by Th68;
end;
