reserve V for non empty RLSStruct;
reserve x,y,y1 for set;
reserve v for VECTOR of V;
reserve a,b for Real;

theorem
  for V being add-associative right_zeroed right_complementable
  non empty addLoopStr, v,w being Element of V holds
  v + w = v or w + v = v implies w = 0.V
proof
  let V be add-associative right_zeroed right_complementable non empty
  addLoopStr, v,w be Element of V;
  assume v + w = v or w + v = v;
  then v + w = v + 0.V or w + v = 0.V + v;
  hence thesis by Th8;
end;
