
theorem Th3:
  for L being add-associative right_zeroed right_complementable Abelian
          non empty addLoopStr,
      a, b, c being Element of L holds a - b - (c - b) = a - c
proof
  let L be add-associative right_zeroed right_complementable Abelian non
  empty addLoopStr, a, b, c be Element of L;
  thus a-b-(c-b) = a-b-c+b by RLVECT_1:29
    .= a-b+b-c by RLVECT_1:28
    .= a-(b-b)-c by RLVECT_1:29
    .= a-0.L-c by RLVECT_1:15
    .= a-c by RLVECT_1:13;
end;
