\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{t30\_stacks\_1 (TMVj2gV2oPsag8jYJcMQNQMUWPAdRT1E4C8)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_stacks\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_stacks\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_stacks\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_stacks\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_stacks\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_stacks\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_stacks\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_stacks\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_stacks\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_stacks\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k12\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_stacks\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k13\_stacks\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_rewrite1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k12\_stacks\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_stacks\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_stacks\_1~\\
X0){\unicdcdcdhd}((v3\_stacks\_1~X0){\unicdcdcdhd}((v4\_stacks\_1~X0){\unicdcdcdhd}((v5\_stacks\_1~X0){\unicdcdcdhd}\\
((v6\_stacks\_1~X0){\unicdcdcdhd}(l1\_stacks\_1~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u4\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(k9\_stacks\_1~X0~(k7\_stacks\_1~X0~X1~X2)=k1\_stacks\_1~(u1\_struct\_0~\\
X0)~(k12\_finseq\_1~(u1\_struct\_0~X0)~X2)~(k9\_stacks\_1~X0~X1))))\end{array}
\label{hyp:ehidpfdhehbgdglgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_stacks\_1~\\
X0){\unicdcdcdhd}((v3\_stacks\_1~X0){\unicdcdcdhd}((v4\_stacks\_1~X0){\unicdcdcdhd}((v5\_stacks\_1~X0){\unicdcdcdhd}\\
((v6\_stacks\_1~X0){\unicdcdcdhd}(l1\_stacks\_1~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u4\_struct\_0~X0)){\unicdbdjdcd}((r1\_stacks\_1~X0~X1){\unicdbdjdcd}(k9\_stacks\_1~X0~X1=\\
k1\_xboole\_0)))\end{array}
\label{hyp:ehfdpfdhehbgdglgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_stacks\_1~\\
X0){\unicdcdcdhd}((v3\_stacks\_1~X0){\unicdcdcdhd}((v4\_stacks\_1~X0){\unicdcdcdhd}((v5\_stacks\_1~X0){\unicdcdcdhd}\\
((v6\_stacks\_1~X0){\unicdcdcdhd}(l1\_stacks\_1~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u4\_struct\_0~X0)){\unicdbdjdcd}(k13\_stacks\_1~X0~X1 \in k11\_stacks\_1~X0~X1))\end{array}
\label{hyp:ehcdjdpfdhehbgdglgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}o .  {\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}(((X0~(k6\_finseq\_1~\\
X1)){\unicdcdcdhd}({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~X1){\unicdbdjdcd}((X0~X2){\unicdbdjdcd}(X0~(k1\_stacks\_1~X1~(k12\_finseq\_1~X1~X3)~X2)))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~X1){\unicdbdjdcd}(X0~X2)))\end{array}
\label{hyp:dhbdpfdhehbgdglgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_finseq\_2~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_2~\\
X2~X0~X1){\unicdbdjdcd}(m2\_finseq\_1~X2~X0))\end{array}
\label{hyp:egehpfngcdpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~\\
X0){\unicdcdcdhd}(l1\_stacks\_1~X0))){\unicdcdcdhd}((m1\_subset\_1~X1~(u4\_struct\_0~X0)){\unicdcdcdhd}(\\
m1\_subset\_1~X2~(u1\_struct\_0~X0)))){\unicdbdjdcd}(m1\_subset\_1~(k7\_stacks\_1~\\
X0~X1~X2)~(u4\_struct\_0~X0))\end{array}
\label{hyp:egehpflghdpfdhehbgdglgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{m1\_finseq\_2}~{({{k3\_finseq\_2}~{X0}})}}~{X0}}}\label{hyp:egehpflgddpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}\\
((v2\_stacks\_1~X0){\unicdcdcdhd}((v3\_stacks\_1~X0){\unicdcdcdhd}((v4\_stacks\_1~X0){\unicdcdcdhd}((v5\_stacks\_1~\\
X0){\unicdcdcdhd}((v6\_stacks\_1~X0){\unicdcdcdhd}(l1\_stacks\_1~X0)))))))){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(u4\_struct\_0~X0))){\unicdbdjdcd}(m1\_subset\_1~(k13\_stacks\_1~X0~X1)~(u4\_struct\_0~\\
X0))\end{array}
\label{hyp:egehpflgbdddpfdhehbgdglgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}\\
((v2\_stacks\_1~X0){\unicdcdcdhd}((v3\_stacks\_1~X0){\unicdcdcdhd}((v4\_stacks\_1~X0){\unicdcdcdhd}((v5\_stacks\_1~\\
X0){\unicdcdcdhd}((v6\_stacks\_1~X0){\unicdcdcdhd}(l1\_stacks\_1~X0)))))))){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(u4\_struct\_0~X0))){\unicdbdjdcd}(m1\_subset\_1~(k11\_stacks\_1~X0~X1)~(k1\_zfmisc\_1~\\
(u4\_struct\_0~X0)))\end{array}
\label{hyp:egehpflgbdbdpfdhehbgdglgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k6\_finseq\_1}~{X0}}={k1\_xboole\_0}}}\label{hyp:eggdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_stacks\_1~\\
X0){\unicdcdcdhd}((v3\_stacks\_1~X0){\unicdcdcdhd}((v4\_stacks\_1~X0){\unicdcdcdhd}((v5\_stacks\_1~X0){\unicdcdcdhd}\\
((v6\_stacks\_1~X0){\unicdcdcdhd}(l1\_stacks\_1~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u4\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u4\_struct\_0~\\
X0)){\unicdbdjdcd}((X2=k13\_stacks\_1~X0~X1){\unicdbdjded}((r1\_stacks\_1~X0~X2){\unicdcdcdhd}({\unicdcdaddd} X3 .  \\
((v5\_relat\_1~X3~(u4\_struct\_0~X0)){\unicdcdcdhd}(m1\_rewrite1~X3~(k12\_stacks\_1~\\
X0))){\unicdcdcdhd}((k1\_funct\_1~X3~np\_\_1=X1){\unicdcdcdhd}((k1\_funct\_1~X3~(k3\_finseq\_1~\\
X3)=X2){\unicdcdcdhd}({\unicdcdadad} X4 .  (v7\_ordinal1~X4){\unicdbdjdcd}((r1\_xxreal\_0~np\_\_1~X4){\unicdbdjdcd}\\
((r1\_xxreal\_0~(k3\_finseq\_1~X3)~X4){\unicdcdcdid}((\preoh r1\_stacks\_1~X0~(k7\_partfun1~\\
(u4\_struct\_0~X0)~X3~X4)){\unicdcdcdhd}(k7\_partfun1~(u4\_struct\_0~X0)~X3~(k1\_nat\_1~\\
X4~np\_\_1)=k5\_stacks\_1~X0~(k7\_partfun1~(u4\_struct\_0~X0)~X3~X4)))))))))))))\end{array}
\label{hyp:egbdjdpfdhehbgdglgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_stacks\_1~\\
X0){\unicdcdcdhd}((v3\_stacks\_1~X0){\unicdcdcdhd}((v4\_stacks\_1~X0){\unicdcdcdhd}((v5\_stacks\_1~X0){\unicdcdcdhd}\\
((v6\_stacks\_1~X0){\unicdcdcdhd}(l1\_stacks\_1~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u4\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(u4\_struct\_0~X0))){\unicdbdjdcd}((X2=k11\_stacks\_1~X0~X1){\unicdbdjded}((X1 \in X2){\unicdcdcdhd}(({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u4\_struct\_0~X0)){\unicdbdjdcd}((X4 \in X2){\unicdbdjdcd}((k7\_stacks\_1~X0~X4~X3 \in X2){\unicdcdcdhd}((\preoh r1\_stacks\_1~\\
X0~X4){\unicdbdjdcd}(k5\_stacks\_1~X0~X4 \in X2)))))){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(u4\_struct\_0~X0))){\unicdbdjdcd}(((X1 \in X3){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u4\_struct\_0~\\
X0)){\unicdbdjdcd}((X5 \in X3){\unicdbdjdcd}((k7\_stacks\_1~X0~X5~X4 \in X3){\unicdcdcdhd}((\preoh r1\_stacks\_1~X0~X5){\unicdbdjdcd}\\
(k5\_stacks\_1~X0~X5 \in X3))))))){\unicdbdjdcd}(r1\_tarski~X2~X3))))))))\end{array}
\label{hyp:egbdhdpfdhehbgdglgdhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddadpfdhehbgdglgdhpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_stacks\_1~\\
X0){\unicdcdcdhd}((v3\_stacks\_1~X0){\unicdcdcdhd}((v4\_stacks\_1~X0){\unicdcdcdhd}((v5\_stacks\_1~X0){\unicdcdcdhd}\\
((v6\_stacks\_1~X0){\unicdcdcdhd}(l1\_stacks\_1~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u4\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_2~X2~(u1\_struct\_0~\\
X0)~(k3\_finseq\_2~(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdaddd} X3 .  (m1\_subset\_1~\\
X3~(u4\_struct\_0~X0)){\unicdcdcdhd}((k9\_stacks\_1~X0~X3=X2){\unicdcdcdhd}(X3 \in k11\_stacks\_1~\\
X0~X1)))))\end{array}$$
\end{theorem}
\end{document}
