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 Satz8p14p2:
  are_orthogonal A,x,A9 iff are_orthogonal A,A9 & A,A9 Is x
  proof
    hereby
      assume
A1:   are_orthogonal A,x,A9;
      hence are_orthogonal A,A9;
      hence A,A9 Is x by A1,Satz8p14p1;
    end;
    assume
A2: are_orthogonal A,A9 & A,A9 Is x;
    then ex y be POINT of S st are_orthogonal A,y,A9;
    hence are_orthogonal A,x,A9 by A2,GTARSKI3:88;
  end;
