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 Th08:
  for a,b being Real st P <> Q & a * (P - Q) = b * (P - Q) holds a = b
  proof
    let a,b be Real;
    assume that
A1: P <> Q and
A2: a * (P - Q) = b * (P - Q);
    P - Q <> 0.V by A1, RLVECT_1:21;
    hence thesis by A2,RLVECT_1:37;
  end;
