reserve a,b,r for non unit non zero Real;
reserve X for non empty set,
        x for Tuple of 4,X;
reserve V             for RealLinearSpace,
        A,B,C,P,Q,R,S for Element of V;

theorem
  for V being RealLinearSpace for P,Q,R being Element of V st
  P,Q,R are_collinear & P <> R & Q <> R & P <> Q holds
  affine-ratio(P,Q,R) <> 0 & affine-ratio(P,Q,R) <> 1 by Th06,Th07;
