reserve F for Field,
  x for Element of F,
  V for VectSp of F,
  v for Element of V;

theorem
  for F being add-associative right_zeroed right_complementable non
empty addLoopStr, a, b being Element of F holds a - b = 0.F implies b - a = 0.
  F
proof
  let F be add-associative right_zeroed right_complementable non empty
  addLoopStr, a,b be Element of F;
  a - b = -(b - a) by RLVECT_1:33;
  hence thesis by Th24;
end;
