\documentclass{article}
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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}
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\begin{document}
\title{t1\_prgcor\_2 (TMPbeKgExR92ci3oo6ae4HSWTqoibtNqW2v)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_prgcor\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k12\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((\\
X0 \in X1){\unicdbdjded}(\preoh r1\_xxreal\_0~X1~X0)))\end{array}
\label{hyp:ehededpfogbgehpfbd}
\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\_afinsq\_1~X0=k1\_card\_1~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfbgggjgogdhbhpfbd}
\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\_card\_1~X0=k9\_xtuple\_0~X0)\end{array}
\label{hyp:jgfgbdpfbgggjgogdhbhpfbd}
\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}(v7\_ordinal1~(k9\_xtuple\_0~X0))\end{array}
\label{hyp:ggdgbdpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v5\_relat\_1~X1~X0){\unicdcdcdhd}((v5\_ordinal1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finset\_1~\\
X1)))))){\unicdbdjdcd}(m2\_finseq\_1~(k12\_afinsq\_1~X0~X1)~X0)\end{array}
\label{hyp:egehpflgbdcdpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v5\_ordinal1~X1){\unicdcdcdhd}\\
((v1\_relat\_1~X1){\unicdcdcdhd}((v5\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finset\_1~\\
X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~X0){\unicdbdjdcd}((r1\_prgcor\_2~X0~X1~X2){\unicdbdjded}\\
((r1\_tarski~k5\_numbers~X0){\unicdcdcdhd}((k1\_funct\_1~X1~k6\_numbers=k3\_finseq\_1~\\
X2){\unicdcdcdhd}((\preoh r1\_xxreal\_0~(k1\_afinsq\_1~X1)~(k3\_finseq\_1~X2)){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
(v7\_ordinal1~X3){\unicdbdjdcd}(((r1\_xxreal\_0~np\_\_1~X3){\unicdcdcdhd}(r1\_xxreal\_0~X3~(k3\_finseq\_1~\\
X2))){\unicdbdjdcd}(k1\_funct\_1~X1~X3=k1\_funct\_1~X2~X3)))))))))\end{array}
\label{hyp:egbdpfahchhgdgpgchpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v5\_relat\_1~X1~X0){\unicdcdcdhd}((v5\_ordinal1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finset\_1~\\
X1))))){\unicdbdjdcd}(((v7\_ordinal1~(k1\_funct\_1~X1~k6\_numbers)){\unicdcdcdhd}(k1\_funct\_1~\\
X1~k6\_numbers \in k1\_afinsq\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~X0){\unicdbdjdcd}\\
((X2=k12\_afinsq\_1~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}((X3=\\
k1\_funct\_1~X1~k6\_numbers){\unicdbdjdcd}((k3\_finseq\_1~X2=X3){\unicdcdcdhd}({\unicdcdadad} X4 .  \\
(v7\_ordinal1~X4){\unicdbdjdcd}(((r1\_xxreal\_0~np\_\_1~X4){\unicdcdcdhd}(r1\_xxreal\_0~X4~X3)){\unicdbdjdcd}\\
(k1\_funct\_1~X2~X4=k1\_funct\_1~X1~X4))))))))))\end{array}
\label{hyp:egbdbdpfbgggjgogdhbhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdpfahchhgdgpgchpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v5\_ordinal1~X1){\unicdcdcdhd}\\
((v1\_relat\_1~X1){\unicdcdcdhd}((v5\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finset\_1~\\
X1))))){\unicdbdjdcd}(((r1\_tarski~k5\_numbers~X0){\unicdcdcdhd}((v7\_ordinal1~(k1\_funct\_1~\\
X1~k6\_numbers)){\unicdcdcdhd}(k1\_funct\_1~X1~k6\_numbers \in k1\_afinsq\_1~X1))){\unicdbdjdcd}\\
(r1\_prgcor\_2~X0~X1~(k12\_afinsq\_1~X0~X1))))\end{array}$$
\end{theorem}
\end{document}
