$j\in \{1,2,\cdots,p\}$, and for $y\in \coprod_{i=1}^{l} (0,1)_i$, let $$f_T(y)=
  \begin{cases}
    0_{l_s}, & \mbox{if } y\in (0,1)_s,\ s\neq i,  \\
    0_{l_i}, & \mbox{if } y\in (0,1)_i,\ y\notin T,  \\
    I_{l_i}, & \mbox{if } y\in (0,1)_i,\ y\in T.
  \end{cases}$$ Set $$E_T(x)=U_x^*\cdot
  \left(
  \begin{array}{ccccccc}
    0&  &  & &  &  &     \\
     & 0 &  & &  &  &   \\
     &  & \ddots & &  &   & \\
     &  &  & 0 &  & &   \\
     &  & &  & f_T(y_1(x)) &  &    \\
     \\
      & &  &  &  & \ddots &  \\
     \\
      & &  &   &  &   & f_T(y_{\bullet}(x))

  \end{array}
  \right)
  \cdot
  U_x.$$ $E_T(x)$ does not depend on $x$ continuously, but $E_T(x)$ commutes with $\phi_x(f)$ for all $f\in A$, if $T_1\cap T_2=\varnothing$, then $E_{T_1}(x)E_{T_2}(x)=0$.

Recall that $\{e_{ss'}^i\}\,(1\leq i\leq l,1\leq s,s' \leq l_i)$ are matrix units of $F_2$. Let $T_i=[\eta,1-\eta]_i\subset Sp(A)$, choose a positive function $\rho$ in $C[0,1]$ with $\rho|_{[\eta,1-\eta]}=1$ and $\rho(0)=\rho(1)=0$, obviously, $\rho e_{ss'}^i\in A$ and the elements $$\overline{e}_{ss'}^i(x):=E_{T_i}(x)\cdot\phi_x(\rho\cdot e_{ss'}^i)\cdot E_{T_i}(x)$$ fulfill the canonical relations for matrix units: $$\overline{e}_{s_1s_1'}^i(x)\cdot\overline{e}_{s_2s_2'}^i(x)=\delta_{s_1's_2}\cdot\overline{e}_{s_1s_2'}^i(x)$$ for all $1\leq s_1,s_2,s_1',s_2'\leq l_i$.

Let $h_r^i$ be the test function corresponding to $V_r^i$. From the pairing results, for any $x_1,x_2,x_3,x_4\in [0,1]\subset Sp(B)$, then we have

$$\begin{aligned}
        \#\big(Sp\phi_{x_1}\cap V_r^i\big) &\leq& \#(\Lambda_1({h_r^i})) \\
      &\leq 