\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}
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\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{t6\_rewrite2 (TMSi1cNw4S9yNsHNJ2srwS6ycZngm3TXfVw)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_rewrite2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_rewrite2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_flang\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_rewrite2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k4\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v5\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_ordinal4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k2\_flang\_1}~{X0}}={{k4\_afinsq\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfggmgbgoghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v5\_ordinal1~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}(v1\_finset\_1~X0)))){\unicdbdjdcd}(k1\_ordinal4~k1\_xboole\_0~X0=X0)\end{array}
\label{hyp:chegcdpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v5\_ordinal1~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}(v1\_finset\_1~X0)))){\unicdbdjdcd}(k1\_ordinal4~X0~k1\_xboole\_0=X0)\end{array}
\label{hyp:chegbdpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~(k4\_afinsq\_1~X0)){\unicdcdcdhd}((v5\_relat\_1~(k4\_afinsq\_1~\\
X0)~X0){\unicdcdcdhd}((v5\_ordinal1~(k4\_afinsq\_1~X0)){\unicdcdcdhd}((v1\_funct\_1~(k4\_afinsq\_1~\\
X0)){\unicdcdcdhd}((v1\_xboole\_0~(k4\_afinsq\_1~X0)){\unicdcdcdhd}(v1\_finset\_1~(k4\_afinsq\_1~\\
X0))))))\end{array}
\label{hyp:ggdgedpfbgggjgogdhbhpfbd}
\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\_rewrite2~\\
X0))){\unicdbdjdcd}(v5\_ordinal1~(k1\_funct\_1~X0~X1))\end{array}
\label{hyp:ggdgddpfchfghhchjgehfgcd}
\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\_rewrite2~\\
X0))){\unicdbdjdcd}((v1\_relat\_1~(k1\_funct\_1~X0~X1)){\unicdcdcdhd}((v1\_funct\_1~(k1\_funct\_1~\\
X0~X1)){\unicdcdcdhd}(v1\_finset\_1~(k1\_funct\_1~X0~X1))))\end{array}
\label{hyp:ggdgcdpfchfghhchjgehfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v5\_ordinal1~X0){\unicdcdcdhd}((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}(v1\_finset\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~\\
X1){\unicdcdcdhd}(v1\_rewrite2~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~\\
X2){\unicdcdcdhd}(v1\_rewrite2~X2))){\unicdbdjdcd}((X2=k2\_rewrite2~X0~X1){\unicdbdjded}((k9\_xtuple\_0~\\
X2=k9\_xtuple\_0~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (X3 \in k9\_xtuple\_0~X1){\unicdbdjdcd}(k1\_funct\_1~\\
X2~X3=k1\_ordinal4~(k1\_funct\_1~X1~X3)~X0))))))\end{array}
\label{hyp:egddpfchfghhchjgehfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v5\_ordinal1~X0){\unicdcdcdhd}((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}(v1\_finset\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~\\
X1){\unicdcdcdhd}(v1\_rewrite2~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~\\
X2){\unicdcdcdhd}(v1\_rewrite2~X2))){\unicdbdjdcd}((X2=k1\_rewrite2~X0~X1){\unicdbdjded}((k9\_xtuple\_0~\\
X2=k9\_xtuple\_0~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (X3 \in k9\_xtuple\_0~X1){\unicdbdjdcd}(k1\_funct\_1~\\
X2~X3=k1\_ordinal4~X0~(k1\_funct\_1~X1~X3)))))))\end{array}
\label{hyp:egcdpfchfghhchjgehfgcd}
\end{equation}
\begin{theorem}\label{thm:ehgdpfchfghhchjgehfgcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_finseq\_1~\\
X1){\unicdcdcdhd}(v1\_rewrite2~X1)))){\unicdbdjdcd}((k1\_rewrite2~(k2\_flang\_1~X0)~X1=X1){\unicdcdcdhd}\\
(k2\_rewrite2~(k2\_flang\_1~X0)~X1=X1))\end{array}$$
\end{theorem}
\end{document}
