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, w,v1,v2 being Element of V st
  w - v1 = w - v2 holds v1 = v2
proof
  let V be add-associative right_zeroed right_complementable non empty
  addLoopStr;
  let w,v1,v2 be Element of V;
  assume w - v1 = w - v2;
  then - v1 = - v2 by Th8;
  hence thesis by Th18;
end;
