theorem Satz8p14p1:
  are_orthogonal A,A9 implies A <> A9
  proof
    assume are_orthogonal A,A9;
    then consider x be POINT of S such that
A1: are_orthogonal A,x,A9;
A2: A is_line & A9 is_line & x in A & x in A9 & (ex u,v being POINT of S st
      u in A & v in A9 & u <> x & v <> x & right_angle u,x,v) by A1,Satz8p13;
    consider u,v be POINT of S such that
A3: u in A and
A4: v in A9 and
A5: u <> x and
A6: v <> x and
A7: right_angle u,x,v by A1,Satz8p13;
    assume A = A9;
    then Collinear u,x,v by A2,A3,A4,GTARSKI3:90;
    hence contradiction by A5,A6,A7,Satz8p9;
  end;
