\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t51\_rvsum\_1 (TMTpqUDSC7ZevMthQEVqqEcm32HY4CK72jU)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k10\_rvsum\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_rvsum\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k24\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_valued\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_valued\_0~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_xcmplx\_0~X2){\unicdbdjdcd}(k24\_valued\_1~(k1\_valued\_1~\\
X0~X1)~X2=k1\_valued\_1~(k24\_valued\_1~X0~X2)~(k24\_valued\_1~X1~X2))))\end{array}
\label{hyp:ehbdgdpfchggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((\\
v3\_valued\_0~X0){\unicdcdcdhd}(v1\_finseq\_1~X0)))){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v3\_valued\_0~X1){\unicdcdcdhd}(v1\_finseq\_1~X1))))){\unicdbdjdcd}(k4\_rvsum\_1~X0~X1=\\
k1\_valued\_1~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfchghdhfhngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((\\
v3\_valued\_0~X0){\unicdcdcdhd}(v1\_finseq\_1~X0)))){\unicdcdcdhd}(v1\_xreal\_0~X1)){\unicdbdjdcd}(k10\_rvsum\_1~\\
X0~X1=k24\_valued\_1~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdadpfchghdhfhngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((\\
v1\_valued\_0~X0){\unicdcdcdhd}(v1\_finseq\_1~X0)))){\unicdcdcdhd}(v1\_xcmplx\_0~X1)){\unicdbdjdcd}((v1\_relat\_1~\\
(k24\_valued\_1~X0~X1)){\unicdcdcdhd}((v1\_funct\_1~(k24\_valued\_1~X0~X1)){\unicdcdcdhd}(v1\_finseq\_1~\\
(k24\_valued\_1~X0~X1))))\end{array}
\label{hyp:ggdgfdedpfghbgmgfhfgegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v3\_valued\_0~\\
X0))){\unicdcdcdhd}(v1\_xreal\_0~X1)){\unicdbdjdcd}((v1\_relat\_1~(k24\_valued\_1~X0~X1)){\unicdcdcdhd}(\\
(v1\_funct\_1~(k24\_valued\_1~X0~X1)){\unicdcdcdhd}(v3\_valued\_0~(k24\_valued\_1~\\
X0~X1))))\end{array}
\label{hyp:ggdgedfdpfghbgmgfhfgegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v3\_valued\_0~\\
X0))){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v3\_valued\_0~X1)))){\unicdbdjdcd}\\
((v1\_relat\_1~(k1\_valued\_1~X0~X1)){\unicdcdcdhd}((v1\_funct\_1~(k1\_valued\_1~\\
X0~X1)){\unicdcdcdhd}(v3\_valued\_0~(k1\_valued\_1~X0~X1))))\end{array}
\label{hyp:ggdgddpfghbgmgfhfgegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((\\
v1\_valued\_0~X0){\unicdcdcdhd}(v1\_finseq\_1~X0)))){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v1\_valued\_0~X1){\unicdcdcdhd}(v1\_finseq\_1~X1))))){\unicdbdjdcd}((v1\_relat\_1~(k1\_valued\_1~\\
X0~X1)){\unicdcdcdhd}((v1\_funct\_1~(k1\_valued\_1~X0~X1)){\unicdcdcdhd}(v1\_finseq\_1~(k1\_valued\_1~\\
X0~X1))))\end{array}
\label{hyp:ggdgbdcdpfghbgmgfhfgegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v3\_valued\_0~X0)){\unicdbdjdcd}((v1\_relat\_1~\\
X0){\unicdcdcdhd}(v1\_valued\_0~X0))\end{array}
\label{hyp:dgdggdpfghbgmgfhfgegpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgddpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehfdbdpfchghdhfhngpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v3\_valued\_0~X1){\unicdcdcdhd}(v1\_finseq\_1~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v3\_valued\_0~X2){\unicdcdcdhd}(v1\_finseq\_1~X2)))){\unicdbdjdcd}\\
(k10\_rvsum\_1~(k4\_rvsum\_1~X1~X2)~X0=k4\_rvsum\_1~(k10\_rvsum\_1~X1~\\
X0)~(k10\_rvsum\_1~X2~X0))))\end{array}$$
\end{theorem}
\end{document}
