theorem
  for V being Abelian add-associative right_zeroed right_complementable
  non empty CLSStruct, L being C_Linear_Combination of V holds Carrier L = {}
  implies Sum L = 0.V
proof
  let V be Abelian add-associative right_zeroed right_complementable non empty
  CLSStruct;
  let L be C_Linear_Combination of V;
  assume Carrier L = {};
  then L = ZeroCLC V by Def3;
  hence thesis by Th11;
end;
