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, c being Element of F holds (b+a)-(c+a) = b-c
proof
  let F be add-associative right_zeroed right_complementable non empty
  addLoopStr, a,b,c be Element of F;
  thus (b+a)-(c+a) = (b+a)+(-a+-c) by RLVECT_1:31
    .= ((b+a)+-a)+-c by RLVECT_1:def 3
    .= (b+(a+-a))+-c by RLVECT_1:def 3
    .= (b+0.F)+-c by RLVECT_1:5
    .= b-c by RLVECT_1:4;
end;
