theorem Th43:
  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,Th34;
    hence x,y '||' f".x,f".y by DIRAF:22;
  end;
  hence thesis by Th34;
end;
