reserve PCPP for CollProjectiveSpace,
  a,a9,a1,a2,a3,b,b9,b1,b2,c,c1,c3,d,d9,e,
  o,p,p1,p2,p3,r,q, q1,q2,q3,x,y for Element of PCPP;

theorem Th1:
  a,b,c are_collinear implies b,c,a are_collinear & c,a,b
  are_collinear & b,a,c are_collinear & a,c,b are_collinear &
c,b,a are_collinear
proof
  assume
A1: a,b,c are_collinear;
  then b,a,c are_collinear by COLLSP:4;
  then
A2: b,c,a are_collinear by COLLSP:4;
  a,c,b are_collinear by A1,COLLSP:4;
  hence thesis by A2,COLLSP:4;
end;
