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 Satz8p15a:
  Collinear a,b,x & are_orthogonal a,b,c,x implies
    are_orthogonal a,b,x,c,x
  proof
    assume
A2: Collinear a,b,x;
    assume
A3: are_orthogonal a,b,c,x;
    then Line(a,b),Line(c,x) Is x
      by A2,LemmaA1,GTARSKI3:def 11,83,Satz8p14p1;
    hence are_orthogonal a,b,x,c,x by A3,Satz8p14p2;
  end;
