reserve x,y for set,
  i for Nat;
reserve V for non empty CLSStruct,
  u,v,v1,v2,v3 for VECTOR of V,
  A for Subset of V,
  l, l1, l2 for C_Linear_Combination of A,
  x,y,y1,y2 for set,
  a,b for Complex,
  F for FinSequence of the carrier of V,
  f for Function of the carrier of V, COMPLEX;
reserve K,L,L1,L2,L3 for C_Linear_Combination of V;

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;
