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);

theorem Th5:
  for K being non empty multMagma
  for a1,a2,a3,b1,b2,b3 being Element of K holds
  mlt(<*a1,a2,a3*>,<*b1,b2,b3*>) = <*a1*b1,a2*b2,a3*b3*>
  proof
    let K be non empty multMagma;
    let a1,a2,a3,b1,b2,b3 be Element of K;
    thus mlt(<*a1,a2,a3*>,<*b1,b2,b3*>)
      = (the multF of K).:(<*a1,a2,a3*>,<*b1,b2,b3*>) by FVSUM_1:def 7
     .= <*a1*b1,a2*b2,a3*b3*> by FINSEQ_2:76;
  end;
