
theorem Th5:
  for V being non empty addLoopStr, l being C_Linear_Combination of
  {}the carrier of V holds l = ZeroCLC V
proof
  let V be non empty addLoopStr;
  let l be C_Linear_Combination of {}(the carrier of V);
  Carrier l c= {} by Def4;
  then Carrier l = {};
  hence thesis by Def3;
end;
