reserve FCPS for up-3-dimensional CollProjectiveSpace;
reserve a,a9,b,b9,c,c9,d,d9,o,p,q,r,s,t,u,x,y,z for Element of FCPS;

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;
