\documentclass{article}
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\newcommand\unicdcdgdad{\not=}
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\begin{document}
\title{t135\_rvsum\_1 (TMUGjv8vCey2zxKtanYgCh1zdrkPwZ29628)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k4\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k23\_rvsum\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_rvsum\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k11\_rvsum\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_2~X1~k1\_numbers~\\
(k4\_finseq\_2~X0~k1\_numbers)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_2~X2~k1\_numbers~\\
(k4\_finseq\_2~X0~k1\_numbers)){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}(k23\_rvsum\_1~\\
(k11\_rvsum\_1~X0~X1~X3)~X2=k11\_binop\_2~X3~(k23\_rvsum\_1~X1~X2)))))\end{array}
\label{hyp:ehbdddbdpfchghdhfhngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_2~X1~k1\_numbers~\\
(k4\_finseq\_2~X0~k1\_numbers)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_2~X2~k1\_numbers~\\
(k4\_finseq\_2~X0~k1\_numbers)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_finseq\_2~X3~k1\_numbers~\\
(k4\_finseq\_2~X0~k1\_numbers)){\unicdbdjdcd}(k23\_rvsum\_1~(k5\_rvsum\_1~X0~X1~X2)~\\
X3=k9\_binop\_2~(k23\_rvsum\_1~X1~X3)~(k23\_rvsum\_1~X2~X3)))))\end{array}
\label{hyp:ehbdddadpfchghdhfhngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_finseq\_2~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_2~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v7\_ordinal1~X0){\unicdbdjdcd}(m1\_finseq\_2~(k4\_finseq\_2~\\
X0~X1)~X1)\end{array}
\label{hyp:egehpflgedpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v7\_ordinal1~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~(k4\_finseq\_2~X0~k1\_numbers)){\unicdcdcdhd}(v1\_xreal\_0~X2))){\unicdbdjdcd}(m2\_finseq\_2~\\
(k11\_rvsum\_1~X0~X1~X2)~k1\_numbers~(k4\_finseq\_2~X0~k1\_numbers))\end{array}
\label{hyp:egehpflgbdbdpfchghdhfhngpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdddfdpfchghdhfhngpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_finseq\_2~X3~k1\_numbers~(k4\_finseq\_2~\\
X0~k1\_numbers)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_finseq\_2~X4~k1\_numbers~(k4\_finseq\_2~\\
X0~k1\_numbers)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m2\_finseq\_2~X5~k1\_numbers~(k4\_finseq\_2~\\
X0~k1\_numbers)){\unicdbdjdcd}(k23\_rvsum\_1~(k5\_rvsum\_1~X0~(k11\_rvsum\_1~X0~X3~\\
X1)~(k11\_rvsum\_1~X0~X4~X2))~X5=k9\_binop\_2~(k11\_binop\_2~X1~(k23\_rvsum\_1~\\
X3~X5))~(k11\_binop\_2~X2~(k23\_rvsum\_1~X4~X5))))))))\end{array}$$
\end{theorem}
\end{document}
