\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{t29\_stacks\_1 (TMatH3VaqyxQKkVWTRSmdSKDP6HYyPGU79g)}
\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 $ k13\_stacks\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_stacks\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_rewrite1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k12\_stacks\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_stacks\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ 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.
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}(k11\_stacks\_1~X0~X1=ReplSep~(toset~({\uniddcgcg} X2 : \\
\iota .  m1\_subset\_1~X2~(u4\_struct\_0~X0)))~({\uniddcgcg} X2 : \iota .  r1\_rewrite1~\\
(k12\_stacks\_1~X0)~X1~X2)~({\uniddcgcg} X2 : \iota .  X2)))\end{array}
\label{hyp:ehcdfdpfdhehbgdglgdhpfbd}
\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 .  ((\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}(m1\_subset\_1~(k12\_stacks\_1~\\
X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u4\_struct\_0~X0)~(u4\_struct\_0~X0))))\end{array}
\label{hyp:egehpflgbdcdpfdhehbgdglgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (r1\_rewrite1~\\
X0~X1~X2){\unicdbdjded}({\unicdcdaddd} X3 .  (m1\_rewrite1~X3~X0){\unicdcdcdhd}((k1\_funct\_1~X3~np\_\_1=\\
X1){\unicdcdcdhd}(k1\_funct\_1~X3~(k3\_finseq\_1~X3)=X2))))\end{array}
\label{hyp:egddpfchfghhchjgehfgbd}
\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 .  {\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:ehcdjdpfdhehbgdglgdhpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_stacks\_1~\\
X0){\unicdcdcdhd}((v3\_stacks\_1~X0){\unicdcdcdhd}((v4\_stacks\_1~X0){\unicdcdcdhd}((v5\_stacks\_1~X0){\unicdcdcdhd}\\
((v6\_stacks\_1~X0){\unicdcdcdhd}(l1\_stacks\_1~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u4\_struct\_0~X0)){\unicdbdjdcd}(k13\_stacks\_1~X0~X1 \in k11\_stacks\_1~X0~X1))\end{array}$$
\end{theorem}
\end{document}
