theorem
  L1 + L2 = ZeroLC(V) implies L2 = - L1
proof
  assume
A1: L1 + L2 = ZeroLC(V);
  let v;
  L1.v + L2.v = ZeroLC(V).v by A1,Th22
    .= 0.GF by Th3;
  hence L2.v = - L1.v by RLVECT_1:6
    .= (- L1).v by Th36;
end;
