reserve a,b,c,d,e,f for Real,
        k,m for Nat,
        D for non empty set,
        V for non trivial RealLinearSpace,
        u,v,w for Element of V,
        p,q,r for Element of ProjectiveSpace(V);
reserve o,p,q,r,s,t for Point of TOP-REAL 3,
        M for Matrix of 3,F_Real;

theorem Th41:
  o,p, (o <X> p) <X> (q <X> r) are_LinDep &
  q,r, (o <X> p) <X> (q <X> r) are_LinDep
  proof
    |{o,p, (o <X> p) <X> (q <X> r)}| = 0 &
    |{q,r, (o <X> p) <X> (q <X> r)}| = 0 by Th40;
    hence thesis by Th37;
  end;
