reserve V for RealLinearSpace;

theorem Th19:
  for L being linear-Functional of V, v1,v2 being VECTOR of V
  holds L.(v1 - v2) = L.v1 - L.v2
proof
  let L be linear-Functional of V, v1,v2 be VECTOR of V;
  thus L.(v1 - v2) = L.(v1) + L.(-v2) by Def2
    .= L.v1 + - L.v2 by Th18
    .= L.v1 - L.v2;
end;
