\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{t46\_stacks\_1 (TMRBTD4nc1uw9J2F4hqpJetqD9zZqzX1GtH)}
\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 $ r4\_stacks\_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 $ r3\_stacks\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k3\_relat\_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 .  ((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}((\preoh v11\_struct\_0~X1){\unicdcdcdhd}((v2\_stacks\_1~X1){\unicdcdcdhd}((v3\_stacks\_1~X1){\unicdcdcdhd}\\
((v4\_stacks\_1~X1){\unicdcdcdhd}((v5\_stacks\_1~X1){\unicdcdcdhd}((v6\_stacks\_1~X1){\unicdcdcdhd}(l1\_stacks\_1~\\
X1)))))))){\unicdbdjdcd}({\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)))))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}(v1\_funct\_1~X3)){\unicdbdjdcd}({\unicdcdadad} X4 .  (\\
(v1\_relat\_1~X4){\unicdcdcdhd}(v1\_funct\_1~X4)){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_relat\_1~X5){\unicdcdcdhd}\\
(v1\_funct\_1~X5)){\unicdbdjdcd}({\unicdcdadad} X6 .  ((v1\_relat\_1~X6){\unicdcdcdhd}(v1\_funct\_1~X6)){\unicdbdjdcd}\\
(((r3\_stacks\_1~X0~X1~X3~X4){\unicdcdcdhd}(r3\_stacks\_1~X1~X2~X5~X6)){\unicdbdjdcd}(r3\_stacks\_1~\\
X0~X2~(k3\_relat\_1~X3~X5)~(k3\_relat\_1~X4~X6)))))))))\end{array}
\label{hyp:ehededpfdhehbgdglgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdcdcdhd}((\\
v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1))){\unicdbdjdcd}((v1\_relat\_1~(k3\_relat\_1~X0~\\
X1)){\unicdcdcdhd}(v1\_funct\_1~(k3\_relat\_1~X0~X1)))\end{array}
\label{hyp:ggdgcdpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{v1\_relat\_1}~{({{{k3\_relat\_1}~{X0}}~{X1}})}}}}\label{hyp:egehpflgddpfchfgmgbgehpfbd}
\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 .  ((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}((\preoh v11\_struct\_0~X1){\unicdcdcdhd}((v2\_stacks\_1~X1){\unicdcdcdhd}((v3\_stacks\_1~X1){\unicdcdcdhd}\\
((v4\_stacks\_1~X1){\unicdcdcdhd}((v5\_stacks\_1~X1){\unicdcdcdhd}((v6\_stacks\_1~X1){\unicdcdcdhd}(l1\_stacks\_1~\\
X1)))))))){\unicdbdjdcd}((r4\_stacks\_1~X0~X1){\unicdbdjded}({\unicdcdaddd} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}\\
(v1\_funct\_1~X2)){\unicdcdcdhd}({\unicdcdaddd} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}(v1\_funct\_1~X3)){\unicdcdcdhd}\\
(r3\_stacks\_1~X0~X1~X2~X3)))))\end{array}
\label{hyp:egcdcdpfdhehbgdglgdhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedgdpfdhehbgdglgdhpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_stacks\_1~\\
X0){\unicdcdcdhd}((v3\_stacks\_1~X0){\unicdcdcdhd}((v4\_stacks\_1~X0){\unicdcdcdhd}((v5\_stacks\_1~X0){\unicdcdcdhd}\\
((v6\_stacks\_1~X0){\unicdcdcdhd}(l1\_stacks\_1~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}((\preoh v11\_struct\_0~X1){\unicdcdcdhd}((v2\_stacks\_1~X1){\unicdcdcdhd}((v3\_stacks\_1~X1){\unicdcdcdhd}\\
((v4\_stacks\_1~X1){\unicdcdcdhd}((v5\_stacks\_1~X1){\unicdcdcdhd}((v6\_stacks\_1~X1){\unicdcdcdhd}(l1\_stacks\_1~\\
X1)))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((\preoh v11\_struct\_0~\\
X2){\unicdcdcdhd}((v2\_stacks\_1~X2){\unicdcdcdhd}((v3\_stacks\_1~X2){\unicdcdcdhd}((v4\_stacks\_1~X2){\unicdcdcdhd}\\
((v5\_stacks\_1~X2){\unicdcdcdhd}((v6\_stacks\_1~X2){\unicdcdcdhd}(l1\_stacks\_1~X2)))))))){\unicdbdjdcd}\\
(((r4\_stacks\_1~X0~X1){\unicdcdcdhd}(r4\_stacks\_1~X1~X2)){\unicdbdjdcd}(r4\_stacks\_1~X0~X2))))\end{array}$$
\end{theorem}
\end{document}
