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 Th13:
  not p,q,r are_collinear implies ex s st not p,q,r,s are_coplanar
proof
  assume
A1: not p,q,r are_collinear;
  consider a,b,c,d such that
A2: not a,b,c,d are_coplanar by Th12;
  assume
A3: not thesis;
  then
A4: p,q,r,c are_coplanar & p,q,r,d are_coplanar;
  p,q,r,a are_coplanar & p,q,r,b are_coplanar by A3;
  hence contradiction by A1,A2,A4,Th8;
end;
