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;

theorem Satz8p2:
  right_angle a,b,c implies right_angle c,b,a
  proof
    assume right_angle a,b,c; then
A1: c,a equiv a,reflection(b,c) by GTARSKI3:6;
    a,reflection(b,c) equiv reflection(b,a),reflection(b,reflection(b,c))
      by GTARSKI3:105;
    then a,reflection(b,c) equiv reflection(b,a),c by GTARSKI3:101;
    then a,reflection(b,c) equiv c,reflection(b,a) by GTARSKI3:7;
    hence thesis by A1,GTARSKI3:5;
end;
