\documentclass{article}
\newtheorem{axiom}{Axiom}
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\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}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t19\_ratfunc1 (TMGSfwxpUBRdcnGaYUoyhzVd7oAob8bGHoP)}
\maketitle
Let $ v7\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l5\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_ratfunc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_ratfunc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_ratfunc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_ratfunc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_algseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_ratfunc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (k1\_xtuple\_0~(k4\_tarski~X0~X1)=X0){\unicdcdcdhd}(k2\_xtuple\_0~\\
(k4\_tarski~X0~X1)=X1)\end{array}
\label{hyp:ehhdpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v7\_struct\_0~X0){\unicdcdcdhd}(l5\_algstr\_0~X0)){\unicdcdcdhd}\\
(m1\_ratfunc1~X1~X0)){\unicdbdjdcd}(k5\_ratfunc1~X0~X1=k2\_xtuple\_0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfchbgehggfhogdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v7\_struct\_0~X0){\unicdcdcdhd}(l5\_algstr\_0~X0)){\unicdcdcdhd}\\
(m1\_ratfunc1~X1~X0)){\unicdbdjdcd}(k4\_ratfunc1~X0~X1=k1\_xtuple\_0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfchbgehggfhogdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v7\_struct\_0~X0){\unicdcdcdhd}(l5\_algstr\_0~\\
X0)){\unicdcdcdhd}(((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~k5\_numbers~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((v1\_algseq\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k5\_numbers~(u1\_struct\_0~X0))))))){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~k5\_numbers~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_algseq\_1~X2~X0){\unicdcdcdhd}((\preoh v1\_ratfunc1~\\
X2~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(\\
u1\_struct\_0~X0)))))))))){\unicdbdjdcd}(k3\_ratfunc1~X0~X1~X2=k4\_tarski~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfchbgehggfhogdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v7\_struct\_0~X0){\unicdcdcdhd}(l5\_algstr\_0~X0)){\unicdcdcdhd}\\
(m1\_ratfunc1~X1~X0)){\unicdbdjdcd}((v1\_funct\_1~(k5\_ratfunc1~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~\\
(k5\_ratfunc1~X0~X1)~k5\_numbers~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_algseq\_1~\\
(k5\_ratfunc1~X0~X1)~X0){\unicdcdcdhd}((\preoh v1\_ratfunc1~(k5\_ratfunc1~X0~X1)~X0){\unicdcdcdhd}\\
(m1\_subset\_1~(k5\_ratfunc1~X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
(u1\_struct\_0~X0))))))))\end{array}
\label{hyp:egehpflgfdpfchbgehggfhogdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v7\_struct\_0~X0){\unicdcdcdhd}(l5\_algstr\_0~X0)){\unicdcdcdhd}\\
(m1\_ratfunc1~X1~X0)){\unicdbdjdcd}((v1\_funct\_1~(k4\_ratfunc1~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~\\
(k4\_ratfunc1~X0~X1)~k5\_numbers~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_algseq\_1~\\
(k4\_ratfunc1~X0~X1)~X0){\unicdcdcdhd}(m1\_subset\_1~(k4\_ratfunc1~X0~X1)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k5\_numbers~(u1\_struct\_0~X0)))))))\end{array}
\label{hyp:egehpflgedpfchbgehggfhogdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}(l5\_algstr\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_ratfunc1~X1~X0){\unicdbdjded}({\unicdcdaddd} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~k5\_numbers~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_algseq\_1~X2~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(u1\_struct\_0~X0))))))){\unicdcdcdhd}\\
({\unicdcdaddd} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~k5\_numbers~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((v1\_algseq\_1~X3~X0){\unicdcdcdhd}((\preoh v1\_ratfunc1~X3~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(u1\_struct\_0~X0)))))))){\unicdcdcdhd}\\
(X1=k4\_tarski~X2~X3))))\end{array}
\label{hyp:egidpfchbgehggfhogdgbd}
\end{equation}
\begin{theorem}\label{thm:ehbdjdpfchbgehggfhogdgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}(l5\_algstr\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_ratfunc1~X1~X0){\unicdbdjdcd}(X1=k3\_ratfunc1~X0~(k4\_ratfunc1~X0~X1)~(k5\_ratfunc1~\\
X0~X1)))\end{array}$$
\end{theorem}
\end{document}
