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 Th23:
  L + ZeroCLC V = L
proof
  let v;
  thus (L + ZeroCLC V).v = L.v + (ZeroCLC V).v by Def8
    .= L.v + 0c by Th2
    .= L.v;
end;
