\documentclass{article}
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\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t48\_comput\_1 (TMYyKS3gd5F3EEzJcLznNvpGEZStuw2tfwN)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_margrel1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_comput\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k19\_margrel1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_recdef\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v3\_margrel1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_rfunct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k2\_comput\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
((v3\_margrel1~X1~X0){\unicdcdcdhd}(m2\_rfunct\_3~X1~(k3\_finseq\_2~X0)~X0~(k2\_comput\_1~\\
X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((v3\_margrel1~X2~X0){\unicdcdcdhd}\\
(m2\_rfunct\_3~X2~(k3\_finseq\_2~X0)~X0~(k2\_comput\_1~X0)))){\unicdbdjdcd}(((k19\_margrel1~\\
X1=k6\_numbers){\unicdcdcdhd}((k19\_margrel1~X2=k6\_numbers){\unicdcdcdhd}(k1\_funct\_1~\\
X1~k1\_xboole\_0=k1\_funct\_1~X2~k1\_xboole\_0))){\unicdbdjdcd}(X1=X2))))\end{array}
\label{hyp:ehedhdpfdgpgngahfhehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~(k3\_finseq\_2~k5\_numbers)){\unicdcdcdhd}\\
((v1\_funct\_1~X0){\unicdcdcdhd}((v4\_valued\_0~X0){\unicdcdcdhd}((v2\_margrel1~X0){\unicdcdcdhd}(v2\_comput\_1~\\
X0)))))){\unicdbdjdcd}((v3\_margrel1~X0~k5\_numbers){\unicdcdcdhd}(m2\_rfunct\_3~X0~(k3\_finseq\_2~\\
k5\_numbers)~k5\_numbers~(k2\_comput\_1~k5\_numbers)))\end{array}
\label{hyp:ehcdjdpfdgpgngahfhehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v4\_valued\_0~\\
X0))){\unicdbdjdcd}(k1\_recdef\_1~X0~X1=k1\_funct\_1~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfchfgdgegfgggpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehedidpfdgpgngahfhehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~\\
X0~(k3\_finseq\_2~k5\_numbers)){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((v4\_valued\_0~\\
X0){\unicdcdcdhd}((v2\_margrel1~X0){\unicdcdcdhd}(v2\_comput\_1~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (\\
(\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~(k3\_finseq\_2~\\
k5\_numbers)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v4\_valued\_0~X1){\unicdcdcdhd}((v2\_margrel1~\\
X1){\unicdcdcdhd}(v2\_comput\_1~X1))))))){\unicdbdjdcd}(((k19\_margrel1~X0=k6\_numbers){\unicdcdcdhd}\\
((k19\_margrel1~X1=k6\_numbers){\unicdcdcdhd}(k1\_recdef\_1~X0~k1\_xboole\_0=\\
k1\_recdef\_1~X1~k1\_xboole\_0))){\unicdbdjdcd}(X0=X1)))\end{array}$$
\end{theorem}
\end{document}
