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 Th44:
  for p,q,r,s be non zero Point of TOP-REAL 3 st
  (p <X> q) <X> (r <X> s) is zero holds
  are_Prop p,q or are_Prop r,s or are_Prop p <X> q,r <X> s
  proof
    let p,q,r,s be non zero Point of TOP-REAL 3;
    assume (p <X> q) <X> (r <X> s) is zero;
    then p <X> q is zero or r <X> s is zero or
      are_Prop p <X> q,r <X> s by Th43;
    hence thesis by Th43;
  end;
