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;
reserve S                 for non empty
                            satisfying_Lower_Dimension_Axiom
                            satisfying_Tarski-model
                            TarskiGeometryStruct,
        a,b,c,p,q,x,y,z,t for POINT of S;

theorem :: ExtPerp:
  for a,b,c,d,x,p,q being POINT of S holds
    c in Line(a,b) & d in Line(a,b) & c <> d &
      are_orthogonal a,b,x,p,q implies are_orthogonal c,d,x,p,q by Prelim11;
