theorem
  are_orthogonal A,x,A9 & are_orthogonal A,y,A9 implies x = y
  proof
    assume that
A1: are_orthogonal A,x,A9 and
A2: are_orthogonal A,y,A9;
    A <> A9 by A1,Satz8p14p1,Satz8p14p2;
    hence thesis by A1,A2,GTARSKI3:89;
  end;
