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 Th16:
  for p1,p2,p3,q1,q2,q3,r1,r2,r3 being Real holds
  <*<*p1,p2,p3*>,<*q1,q2,q3*>,<*r1,r2,r3*>*> is Matrix of 3,F_Real
  proof
    let p1,p2,p3,q1,q2,q3,r1,r2,r3 be Real;
    reconsider P1 = p1,P2 = p2,P3 = p3,
    Q1 = q1,Q2 = q2,Q3 = q3,
    R1 = r1,R2 = r2,R3 = r3 as Element of F_Real by XREAL_0:def 1;
    <*<*P1,P2,P3*>,<*Q1,Q2,Q3*>,<*R1,R2,R3*>*> is Matrix of 3,F_Real
      by MATRIXR2:35;
    hence thesis;
  end;
