theorem Th22:
  (L1+L2).v = L1.v + L2.v
  proof
    dom L1 = the carrier of V & dom L2 = the carrier of V by FUNCT_2:def 1;
    then
A1: L1/.v = L1.v & L2/.v = L2.v by PARTFUN1:def 6;
A2: dom (L1+L2) = the carrier of V by FUNCT_2:def 1;
    hence (L1+L2).v = (L1+L2)/.v by PARTFUN1:def 6
    .= L1.v + L2.v by A1,A2,VFUNCT_1:def 1;
  end;
