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
  not a,b,c are_collinear & a,b,c,p are_coplanar & a,b,c,q are_coplanar &
  a,b,c,r are_coplanar & a,b,c,s are_coplanar implies
  ex x st p,q,x are_collinear & r,s,x are_collinear
  proof
    assume not a,b,c are_collinear & a,b,c,p are_coplanar &
    a,b,c,q are_coplanar & a,b,c,r are_coplanar & a,b,c,s are_coplanar;
    then p,q,r,s are_coplanar by Th8;
    hence thesis;
  end;
