reserve S for non empty satisfying_Tarski-model
              TarskiGeometryStruct,
        a,b,c,d,c9,x,y,z,p,q,q9 for POINT of S;
reserve              S for satisfying_Tarski-model TarskiGeometryStruct,
        a,a9,b,b9,c,c9 for POINT of S;
reserve S                 for non empty satisfying_Tarski-model
                                    TarskiGeometryStruct,
        A,A9              for Subset of S,
        x,y,z,a,b,c,c9,d,u,p,q,q9 for POINT of S;

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;
