  b(00) , \quad  b'(00) := 0 , \quad  b'(00) := 0 .\end{aligned}$$ We also update the tuple $\tau({\Delta})$ according to the information that ${\Delta}(\Omega)$ contains a face $\Pi_b$ such that ${\varphi}({\partial}\Pi_b) \equiv  a_{b(0)}^{-{\varepsilon}_0}$.  The case of an extension of type 0 on the left is complete.  Suppose that a [pseudobracket]{} $b' \in B_{i+0}$, $i \ge 0$, is obtained from $b \in B_{i}$ by an extension of type 0 on the right. This case is similar to its "left" analogue 