\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{t41\_stacks\_1 (TMZ4VEwCy4wnWnpT3f6BtY5ZbfEerYaPMxp)}
\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 $ k14\_stacks\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k10\_stacks\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_stacks\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\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 $ v1\_stacks\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k8\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_stacks\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_stacks\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_stacks\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ u3\_stacks\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_filter\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_stacks\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k6\_partfun1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_orders\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u4\_stacks\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_funct\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k3\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ g1\_stacks\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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}({\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}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u4\_struct\_0~(k14\_stacks\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~(k14\_stacks\_1~\\
X0))){\unicdbdjdcd}(((X3=k6\_eqrel\_1~(u4\_struct\_0~X0)~(u4\_struct\_0~X0)~(k10\_stacks\_1~\\
X0)~X1){\unicdcdcdhd}(X4=X2)){\unicdbdjdcd}((k7\_stacks\_1~X0~X1~X2 \in k7\_stacks\_1~(k14\_stacks\_1~\\
X0)~X3~X4){\unicdcdcdhd}(k6\_eqrel\_1~(u4\_struct\_0~X0)~(u4\_struct\_0~X0)~(k10\_stacks\_1~\\
X0)~(k7\_stacks\_1~X0~X1~X2)=k7\_stacks\_1~(k14\_stacks\_1~X0)~X3~X4)))))))\end{array}
\label{hyp:ehddidpfdhehbgdglgdhpfbd}
\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~\\
(k14\_stacks\_1~X0))){\unicdbdjdcd}((X2=k6\_eqrel\_1~(u4\_struct\_0~X0)~(u4\_struct\_0~\\
X0)~(k10\_stacks\_1~X0)~X1){\unicdbdjdcd}((r1\_stacks\_1~X0~X1){\unicdbdjded}(r1\_stacks\_1~(\\
k14\_stacks\_1~X0)~X2)))))\end{array}
\label{hyp:ehddgdpfdhehbgdglgdhpfbd}
\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}(m1\_subset\_1~(k6\_eqrel\_1~(u4\_struct\_0~X0)~\\
(u4\_struct\_0~X0)~(k10\_stacks\_1~X0)~X1)~(u4\_struct\_0~(k14\_stacks\_1~\\
X0))))\end{array}
\label{hyp:ehddfdpfdhehbgdglgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}o .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X2){\unicdcdcdhd}\\
((\preoh v11\_struct\_0~X2){\unicdcdcdhd}((v2\_stacks\_1~X2){\unicdcdcdhd}((v3\_stacks\_1~X2){\unicdcdcdhd}((\\
v4\_stacks\_1~X2){\unicdcdcdhd}((v5\_stacks\_1~X2){\unicdcdcdhd}((v6\_stacks\_1~X2){\unicdcdcdhd}(l1\_stacks\_1~\\
X2)))))))){\unicdcdcdhd}(m1\_subset\_1~X1~(u4\_struct\_0~X2))){\unicdbdjdcd}((({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u4\_struct\_0~X2)){\unicdbdjdcd}((r1\_stacks\_1~X2~X3){\unicdbdjdcd}(X0~X3))){\unicdcdcdhd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u4\_struct\_0~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~X2)){\unicdbdjdcd}((X0~X3){\unicdbdjdcd}(X0~(k7\_stacks\_1~X2~X3~X4)))))){\unicdbdjdcd}\\
(X0~X1))\end{array}
\label{hyp:dhddpfdhehbgdglgdhpfbd}
\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}((v1\_stacks\_1~(k14\_stacks\_1~\\
X0)){\unicdcdcdhd}(v6\_stacks\_1~(k14\_stacks\_1~X0)))\end{array}
\label{hyp:ggdgbdhdpfdhehbgdglgdhpfbd}
\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}((v1\_stacks\_1~(k14\_stacks\_1~\\
X0)){\unicdcdcdhd}(v5\_stacks\_1~(k14\_stacks\_1~X0)))\end{array}
\label{hyp:ggdgbdgdpfdhehbgdglgdhpfbd}
\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}((v1\_stacks\_1~(k14\_stacks\_1~\\
X0)){\unicdcdcdhd}(v4\_stacks\_1~(k14\_stacks\_1~X0)))\end{array}
\label{hyp:ggdgbdfdpfdhehbgdglgdhpfbd}
\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}((v1\_stacks\_1~(k14\_stacks\_1~\\
X0)){\unicdcdcdhd}(v3\_stacks\_1~(k14\_stacks\_1~X0)))\end{array}
\label{hyp:ggdgbdedpfdhehbgdglgdhpfbd}
\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}((v1\_stacks\_1~(k14\_stacks\_1~\\
X0)){\unicdcdcdhd}(v2\_stacks\_1~(k14\_stacks\_1~X0)))\end{array}
\label{hyp:ggdgbdddpfdhehbgdglgdhpfbd}
\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}((\preoh v2\_struct\_0~(\\
k14\_stacks\_1~X0)){\unicdcdcdhd}((\preoh v11\_struct\_0~(k14\_stacks\_1~X0)){\unicdcdcdhd}(v1\_stacks\_1~\\
(k14\_stacks\_1~X0))))\end{array}
\label{hyp:ggdgbdcdpfdhehbgdglgdhpfbd}
\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}((v1\_stacks\_1~(k14\_stacks\_1~\\
X0)){\unicdcdcdhd}(l1\_stacks\_1~(k14\_stacks\_1~X0)))\end{array}
\label{hyp:egehpflgbdedpfdhehbgdglgdhpfbd}
\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 .  ((v1\_stacks\_1~\\
X1){\unicdcdcdhd}(l1\_stacks\_1~X1)){\unicdbdjdcd}((X1=k14\_stacks\_1~X0){\unicdbdjded}((u1\_struct\_0~\\
X1=u1\_struct\_0~X0){\unicdcdcdhd}((u4\_struct\_0~X1=k8\_eqrel\_1~(u4\_struct\_0~\\
X0)~(k10\_stacks\_1~X0)){\unicdcdcdhd}((u1\_stacks\_1~X1=k6\_domain\_1~(k1\_zfmisc\_1~\\
(u4\_struct\_0~X0))~(u1\_stacks\_1~X0)){\unicdcdcdhd}((u2\_stacks\_1~X1=k3\_stacks\_1~\\
(u1\_struct\_0~X0)~(u4\_struct\_0~X0)~(k10\_stacks\_1~X0)~(u2\_stacks\_1~\\
X0)){\unicdcdcdhd}((u3\_stacks\_1~X1=k2\_filter\_1~(u4\_struct\_0~X0)~(k10\_stacks\_1~\\
X0)~(k4\_stacks\_1~(u4\_struct\_0~X0)~(u4\_struct\_0~X0)~(u1\_stacks\_1~\\
X0)~(u1\_stacks\_1~X0)~(u3\_stacks\_1~X0)~(k6\_partfun1~(u1\_stacks\_1~\\
X0)))){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_orders\_1~X2~(k8\_eqrel\_1~(u4\_struct\_0~\\
X0)~(k10\_stacks\_1~X0))){\unicdbdjdcd}(u4\_stacks\_1~X1=k2\_funct\_7~(k1\_partfun1~\\
(k8\_eqrel\_1~(u4\_struct\_0~X0)~(k10\_stacks\_1~X0))~(k3\_tarski~(k8\_eqrel\_1~\\
(u4\_struct\_0~X0)~(k10\_stacks\_1~X0)))~(u4\_struct\_0~X0)~(u1\_struct\_0~\\
X0)~X2~(u4\_stacks\_1~X0))~(u1\_stacks\_1~X0)~(the~({\uniddcgcg} X3 : \iota .  m1\_subset\_1~\\
X3~(u1\_struct\_0~X0))))))))))))\end{array}
\label{hyp:egcdadpfdhehbgdglgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_stacks\_1~X0){\unicdbdjdcd}((v1\_stacks\_1~X0){\unicdbdjdcd}(X0=g1\_stacks\_1~\\
(u1\_struct\_0~X0)~(u4\_struct\_0~X0)~(u1\_stacks\_1~X0)~(u2\_stacks\_1~\\
X0)~(u3\_stacks\_1~X0)~(u4\_stacks\_1~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfdhehbgdglgdhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedbdpfdhehbgdglgdhpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_stacks\_1~\\
X0){\unicdcdcdhd}((v3\_stacks\_1~X0){\unicdcdcdhd}((v4\_stacks\_1~X0){\unicdcdcdhd}((v5\_stacks\_1~X0){\unicdcdcdhd}\\
((v6\_stacks\_1~X0){\unicdcdcdhd}(l1\_stacks\_1~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u4\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u4\_struct\_0~\\
(k14\_stacks\_1~X0))){\unicdbdjdcd}((X2=k6\_eqrel\_1~(u4\_struct\_0~X0)~(u4\_struct\_0~\\
X0)~(k10\_stacks\_1~X0)~X1){\unicdbdjdcd}(k9\_stacks\_1~(k14\_stacks\_1~X0)~X2=k9\_stacks\_1~\\
X0~X1))))\end{array}$$
\end{theorem}
\end{document}
