\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{t2\_msaterm (TMaWu8Dk6zxqci5tNti81RAPkFbY2m8gPDG)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_dtconstr : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k5\_msafree : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_trees\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_msaterm : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_msafree : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_trees\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ l1\_lang1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_trees\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_dtconstr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_dtconstr : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_msaterm : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v2\_dtconstr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_dtconstr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_lang1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_trees\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_trees\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_funct\_1 : {{\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}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~X0))))){\unicdbdjdcd}\\
((r1\_tarski~(k2\_lang1~(k5\_msafree~X0~X1))~(k2\_zfmisc\_1~(u4\_struct\_0~\\
X0)~(k1\_tarski~(u1\_struct\_0~X0)))){\unicdcdcdhd}((r1\_tarski~(k3\_card\_3~(k3\_msafree~\\
(u1\_struct\_0~X0)~X1))~(k1\_lang1~(k5\_msafree~X0~X1))){\unicdcdcdhd}((v2\_relat\_1~\\
X1){\unicdbdjdcd}((k2\_lang1~(k5\_msafree~X0~X1)=k2\_zfmisc\_1~(u4\_struct\_0~X0)~\\
(k1\_tarski~(u1\_struct\_0~X0))){\unicdcdcdhd}(k1\_lang1~(k5\_msafree~X0~X1)=k3\_card\_3~\\
(k3\_msafree~(u1\_struct\_0~X0)~X1)))))))\end{array}
\label{hyp:ehgdpfngdhbgggchfgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_trees\_1~X0)){\unicdbdjdcd}((k1\_xboole\_0 \in \\
X0){\unicdcdcdhd}(k6\_finseq\_1~k5\_numbers \in X0))\end{array}
\label{hyp:ehcdcdpfehchfgfgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_lang1~X0)){\unicdbdjdcd}(k2\_xboole\_0~(\\
k1\_lang1~X0)~(k2\_lang1~X0)=u1\_struct\_0~X0)\end{array}
\label{hyp:ehbdpfmgbgoghgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}(m1\_trees\_3~X1~X0)){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(\\
k1\_zfmisc\_1~X1))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_dtconstr~X3~X0~X1~X2){\unicdbdjded}(m1\_subset\_1~\\
X3~X2))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngbdpfegehdgpgogdhehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_dtconstr~X0){\unicdcdcdhd}(l1\_lang1~X0))){\unicdbdjdcd}\\
(k6\_dtconstr~X0=k1\_lang1~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfegehdgpgogdhehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~X0))){\unicdcdcdhd}(((v1\_relat\_1~X1){\unicdcdcdhd}\\
((v2\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_funct\_1~\\
X1){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~X0)))))){\unicdcdcdhd}((m1\_subset\_1~X2~(\\
k1\_msaterm~X0~X1)){\unicdcdcdhd}(m1\_subset\_1~X3~(k9\_xtuple\_0~X2))))){\unicdbdjdcd}(k3\_msaterm~\\
X0~X1~X2~X3=k1\_funct\_1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfngdhbgehfgchng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v2\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~\\
X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (\preoh (X2 \in k6\_dtconstr~(k5\_msafree~X0~X1)){\unicdcdcdhd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(k1\_funct\_1~X1~X3)){\unicdbdjdcd}(X2{\unicdcdgdad}k4\_tarski~X4~X3)))){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_funct\_1~\\
X1~X3)){\unicdbdjdcd}((X2=k4\_tarski~X4~X3){\unicdbdjdcd}(X2 \in k6\_dtconstr~(k5\_msafree~X0~\\
X1)))))))\end{array}
\label{hyp:mggdpfngdhbgehfgchng}
\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}\\
(l1\_msualg\_1~X0))){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v2\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~\\
X0))))))){\unicdbdjdcd}((v1\_dtconstr~(k5\_msafree~X0~X1)){\unicdcdcdhd}((v2\_dtconstr~(\\
k5\_msafree~X0~X1)){\unicdcdcdhd}(v3\_dtconstr~(k5\_msafree~X0~X1))))\end{array}
\label{hyp:ggdggdpfngdhbgggchfgfg}
\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}\\
(l1\_msualg\_1~X0))){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~X0)))))){\unicdbdjdcd}\\
((\preoh v2\_struct\_0~(k5\_msafree~X0~X1)){\unicdcdcdhd}(v1\_lang1~(k5\_msafree~X0~X1)))\end{array}
\label{hyp:ggdgfdpfngdhbgggchfgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v3\_trees\_2~X0))){\unicdbdjdcd}\\
((\preoh v1\_xboole\_0~(k9\_xtuple\_0~X0)){\unicdcdcdhd}(v1\_trees\_1~(k9\_xtuple\_0~X0)))\end{array}
\label{hyp:ggdgcdpfehchfgfgdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdgcdpfdhehchfhdgehpfad}
\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}\\
(l1\_msualg\_1~X0))){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v2\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~\\
X0))))))){\unicdbdjdcd}(\preoh v1\_xboole\_0~(k1\_msaterm~X0~X1))\end{array}
\label{hyp:ggdgbdpfngdhbgehfgchng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_trees\_3~X1~X0){\unicdbdjdcd}\\
(\preoh v1\_xboole\_0~X1))\end{array}
\label{hyp:egehpfngbdpfehchfgfgdhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}(m1\_trees\_3~X1~X0)){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(\\
k1\_zfmisc\_1~X1))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_dtconstr~X3~X0~X1~X2){\unicdbdjdcd}(m1\_subset\_1~\\
X3~X1))\end{array}
\label{hyp:egehpfngbdpfegehdgpgogdhehch}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_lang1}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfmgbgoghgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({\preoh{{{v1\_xboole\_0}~{X0}}}})}{\unicdbdjdcd}{({{{m1\_trees\_3}~{({{k5\_trees\_3}~{X0}})}}~{X0}})}}}\label{hyp:egehpflgfdpfehchfgfgdhpfdd}
\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}\\
(l1\_msualg\_1~X0))){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~X0)))))){\unicdbdjdcd}\\
(l1\_lang1~(k5\_msafree~X0~X1))\end{array}
\label{hyp:egehpflgfdpfngdhbgggchfgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~X0))){\unicdcdcdhd}(((v1\_relat\_1~X1){\unicdcdcdhd}\\
((v2\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_funct\_1~\\
X1){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~X0)))))){\unicdcdcdhd}((m1\_subset\_1~X2~(\\
k1\_msaterm~X0~X1)){\unicdcdcdhd}(m1\_subset\_1~X3~(k9\_xtuple\_0~X2))))){\unicdbdjdcd}(m1\_subset\_1~\\
(k3\_msaterm~X0~X1~X2~X3)~(u1\_struct\_0~(k5\_msafree~X0~X1)))\end{array}
\label{hyp:egehpflgddpfngdhbgehfgchng}
\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}\\
(l1\_msualg\_1~X0))){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~X0)))))){\unicdbdjdcd}\\
(m1\_subset\_1~(k1\_msaterm~X0~X1)~(k1\_zfmisc\_1~(k5\_trees\_3~(u1\_struct\_0~\\
(k5\_msafree~X0~X1)))))\end{array}
\label{hyp:egehpflgbdpfngdhbgehfgchng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k4\_tarski~X0~X1=k2\_tarski~(k2\_tarski~X0~\\
X1)~(k1\_tarski~X0)\end{array}
\label{hyp:egfdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k2\_xboole\_0~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}((X3 \in X0){\unicdcdcdid}(X3 \in X1)))\end{array}
\label{hyp:egddpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_tarski}~{X0}}~{X1}}={{{k2\_tarski}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v3\_trees\_3~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~X0){\unicdbdjdcd}(v3\_trees\_2~X1))\end{array}
\label{hyp:dgdgjdpfehchfgfgdhpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v3\_trees\_3}~{X0}})}{\unicdbdjdcd}{({{v4\_funct\_1}~{X0}})}}}\label{hyp:dgdgidpfehchfgfgdhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v4\_funct\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}(\\
(v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)))\end{array}
\label{hyp:dgdgidpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_trees\_3~X1~X0){\unicdbdjdcd}\\
(v3\_trees\_3~X1))\end{array}
\label{hyp:dgdgbdadpfehchfgfgdhpfdd}
\end{equation}
\begin{theorem}\label{thm:ehcdpfngdhbgehfgchng}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v2\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~\\
X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_dtconstr~X2~(u1\_struct\_0~(k5\_msafree~\\
X0~X1))~(k5\_trees\_3~(u1\_struct\_0~(k5\_msafree~X0~X1)))~(k1\_msaterm~\\
X0~X1)){\unicdbdjdcd}(\preoh ({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(k1\_funct\_1~X1~X3)){\unicdbdjdcd}(k1\_funct\_1~X2~k1\_xboole\_0{\unicdcdgdad}\\
k4\_tarski~X4~X3))){\unicdcdcdhd}(\preoh k1\_funct\_1~X2~k1\_xboole\_0 \in k2\_zfmisc\_1~(\\
u4\_struct\_0~X0)~(k1\_tarski~(u1\_struct\_0~X0))))))\end{array}$$
\end{theorem}
\end{document}
