Equation 16.3.3735F5A4FBAC68

\begin{equation} \begin{aligned} \theta _{\varphi _ C}^ n=& \mathds {1}_{\{ \varphi >\gamma -C\} } \, \theta _{\varphi _ C}^ n+ \mathds {1}_{\{ \varphi \leq \gamma -C\} } \, \theta _{\varphi _ C}^ n & \\ =& \mathds {1}_{\{ \varphi >\gamma -C\} } \, \theta _{\varphi }^ n+ \mathds {1}_{\{ \varphi \leq \gamma -C\} } \, \theta _{\varphi _ C}^ n & \textup{by proposition \href{../../tag/9E81D36B1290/}{13.11.4} \href{../../tag/9E81D36B1290/#sgpt-1C036AD6}{1}}\\ =& \theta _{\varphi }^ n+ \mathds {1}_{\{ \varphi \leq \gamma -C\} } \, \theta _{\varphi _ C}^ n & \textup{by theorem \href{../../tag/553335F185CE/}{16.3.12}}. \end{aligned} \end{equation}