\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=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t23\_stacks\_1 (TMQbWg56cjkHrHwcYL7VywrwNuoJRH92Pfi)}
\maketitle
Let $ v1\_xboole\_0 : {{\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 $ m1\_rewrite1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
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 $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_0 : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_rewrite1~X2~X1){\unicdbdjdcd}((k1\_funct\_1~\\
X2~np\_\_1 \in X0){\unicdbdjdcd}(m2\_finseq\_1~X2~X0))))\end{array}
\label{hyp:ehhdddpfbgcgdgngjgkhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}(v1\_finseq\_1~X0)))){\unicdbdjdcd}((np\_\_1 \in k4\_finseq\_1~X0){\unicdcdcdhd}(k3\_finseq\_1~\\
X0 \in k4\_finseq\_1~X0))\end{array}
\label{hyp:ehgdpfggjgogdhfgbhpffd}
\end{equation}
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}
{{{k1\_card\_1}~{k1\_xboole\_0}}={k1\_xboole\_0}}\label{hyp:ehcdhdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v5\_relat\_1~X1~X0){\unicdcdcdhd}(\\
v1\_funct\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (X2 \in k9\_xtuple\_0~X1){\unicdbdjdcd}(k1\_funct\_1~\\
X1~X2 \in X0))\end{array}
\label{hyp:ehbdadcdpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{np\_\_0}}\label{hyp:dhahdgadpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{{r1\_xxreal\_0}~{np\_\_0}}~{np\_\_0}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchadpfchad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))){\unicdbdjdcd}\\
(k4\_finseq\_1~X0=k9\_xtuple\_0~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))){\unicdbdjdcd}\\
(k3\_finseq\_1~X0=k1\_card\_1~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}(((\\
v5\_relat\_1~X1~X0){\unicdcdcdhd}(v1\_finseq\_1~X1)){\unicdbdjdcd}(m2\_finseq\_1~X1~X0))\end{array}
\label{hyp:mgfdpfggpgngpgegfgmgad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_rewrite1~X1~X0){\unicdbdjdcd}(\\
(v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~X1))))\end{array}
\label{hyp:egehpfngbdpfchfghhchjgehfgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~\\
X1){\unicdcdcdhd}(v1\_finseq\_1~X1))){\unicdbdjdcd}((m1\_rewrite1~X1~X0){\unicdbdjded}((\preoh r1\_xxreal\_0~\\
(k3\_finseq\_1~X1)~k6\_numbers){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}\\
(((X2 \in k4\_finseq\_1~X1){\unicdcdcdhd}(k2\_nat\_1~X2~np\_\_1 \in k4\_finseq\_1~X1)){\unicdbdjdcd}(\\
k4\_tarski~(k1\_funct\_1~X1~X2)~(k1\_funct\_1~X1~(k2\_nat\_1~X2~np\_\_1)) \in \\
X0))))))\end{array}
\label{hyp:egcdpfchfghhchjgehfgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjded}{({{\unicdcdadad} X1 .  {\preoh{{{X1} \in {X0}}}}})}}}\label{hyp:egbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m1\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjdcd}{({{{v5\_relat\_1}~{X1}}~{X0}})}}}}\label{hyp:dgdgddpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v1\_relat\_1~X2)\end{array}
\label{hyp:dgdgbdpfchfgmgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdddpfdhehbgdglgdhpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_rewrite1~X2~X1){\unicdbdjdcd}((k1\_funct\_1~\\
X2~np\_\_1 \in X0){\unicdbdjded}(v5\_relat\_1~X2~X0))))\end{array}$$
\end{theorem}
\end{document}
