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 Abelian add-associative right_zeroed right_complementable
  non empty addLoopStr, v,u,w being Element of V holds v - (u - w) = (v -u) + w
proof
  let V be Abelian add-associative right_zeroed right_complementable non
  empty addLoopStr;
  let v,u,w be Element of V;
  thus v - (u - w) = v - (u + - w) .= (v - u) - - w by Th27
    .= (v - u) + w;
end;
