  \begin{align*}
    \bigg|\int_s^t X^n_{u-} \otimes \d X_u - X_{s} \otimes X_{s,t}\bigg| &\leq 2 \bigg\|\int_0^{\cdot} X^n_{u-} \otimes \d X_u - \int_0^{\cdot} X_{u-} \otimes \d X_u\bigg\|_{\infty,[0,T]} + |\mathbb{X}_{s,t}|\\
    &\leq C_2 \Big(2^{-n(1-\varepsilon)} + w_{\mathbb{X},\frac{p}{2}}(s,t)^{\frac{2}{p}}\Big)\\
    &\leq C_2 \Big(w_{X,q_0}(s,t)^{\frac{2}{p}} + w_{\mathbb{X},\frac{p}{2}}(s,t)^{\frac{2}{p}}\Big)
  \end{align*}
