theorem Satz8p3:
  right_angle a,b,c & a <> b & Collinear b,a,a9 implies right_angle a9,b,c
  proof
    assume that
A1: right_angle a,b,c and
A2: a <> b and
A3: Collinear b,a,a9;
    now
      b,c equiv reflection(b,b),reflection(b,c) by GTARSKI3:105;
      hence b,c equiv b,reflection(b,c) by Lem01;
    end;
    hence thesis by A1,A2,A3,GTARSKI3:53;
  end;
