theorem
  L1 + L2 = ZeroCLC V implies L2 = - L1
proof
  assume
A1: L1 + L2 = ZeroCLC V;
  let v;
  L1.v + L2.v = (ZeroCLC V).v by A1,Def8
    .= 0c by Th2;
  hence L2.v = - L1.v .= (- L1).v by Th31;
end;
