\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{t39\_msaterm (TMP2Zg1mNGDvA1BDJKNDdHcNoXSCdaddunu)}
\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 $ v4\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m4\_msaterm : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m2\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ 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 $ k2\_pboole : {{\iota}{\unicdbdjdcd}{{\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 $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_trees\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_msaterm : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}$ be given.
Let $ k9\_msaterm : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k7\_msaterm : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m1\_subset\_1 : {{\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}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v4\_msualg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m4\_msaterm~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_dtconstr~X3~\\
(u1\_struct\_0~(k5\_msafree~X0~(k2\_pboole~(u1\_struct\_0~X0)~(u3\_msualg\_1~\\
X0~X1)~X2)))~(k5\_trees\_3~(u1\_struct\_0~(k5\_msafree~X0~(k2\_pboole~\\
(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~X2))))~(k1\_msaterm~X0~(k2\_pboole~\\
(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~X2))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_pboole~\\
X4~(u1\_struct\_0~X0)~X2~(u3\_msualg\_1~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_relat\_1~\\
X5){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_finset\_1~X5){\unicdcdcdhd}(v3\_trees\_2~X5)))){\unicdbdjdcd}\\
((r1\_msaterm~X0~X1~X2~X3~X4~X5){\unicdbdjdcd}(k1\_funct\_1~X5~k1\_xboole\_0 \in k1\_funct\_1~\\
(u3\_msualg\_1~X0~X1)~(k7\_msaterm~X0~(k2\_pboole~(u1\_struct\_0~X0)~\\
(u3\_msualg\_1~X0~X1)~X2)~X3))))))))\end{array}
\label{hyp:ehddidpfngdhbgehfgchng}
\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}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v4\_msualg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m4\_msaterm~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_dtconstr~X3~\\
(u1\_struct\_0~(k5\_msafree~X0~(k2\_pboole~(u1\_struct\_0~X0)~(u3\_msualg\_1~\\
X0~X1)~X2)))~(k5\_trees\_3~(u1\_struct\_0~(k5\_msafree~X0~(k2\_pboole~\\
(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~X2))))~(k1\_msaterm~X0~(k2\_pboole~\\
(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~X2))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_pboole~\\
X4~(u1\_struct\_0~X0)~X2~(u3\_msualg\_1~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~(k1\_funct\_1~(u3\_msualg\_1~X0~X1)~(k7\_msaterm~X0~(k2\_pboole~(u1\_struct\_0~\\
X0)~(u3\_msualg\_1~X0~X1)~X2)~X3))){\unicdbdjdcd}((X5=k9\_msaterm~X0~X1~X2~X3~X4){\unicdbdjded}\\
({\unicdcdaddd} X6 .  ((v1\_relat\_1~X6){\unicdcdcdhd}((v1\_funct\_1~X6){\unicdcdcdhd}((v1\_finset\_1~\\
X6){\unicdcdcdhd}(v3\_trees\_2~X6)))){\unicdcdcdhd}((r1\_msaterm~X0~X1~X2~X3~X4~X6){\unicdcdcdhd}(X5=k1\_funct\_1~\\
X6~k1\_xboole\_0)))))))))\end{array}
\label{hyp:egbdadpfngdhbgehfgchng}
\end{equation}
\begin{theorem}\label{thm:ehddjdpfngdhbgehfgchng}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v4\_msualg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m4\_msaterm~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_pboole~X3~(u1\_struct\_0~\\
X0)~X2~(u3\_msualg\_1~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_dtconstr~X4~(u1\_struct\_0~\\
(k5\_msafree~X0~(k2\_pboole~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~\\
X2)))~(k5\_trees\_3~(u1\_struct\_0~(k5\_msafree~X0~(k2\_pboole~(u1\_struct\_0~\\
X0)~(u3\_msualg\_1~X0~X1)~X2))))~(k1\_msaterm~X0~(k2\_pboole~(u1\_struct\_0~\\
X0)~(u3\_msualg\_1~X0~X1)~X2))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_relat\_1~X5){\unicdcdcdhd}((\\
v1\_funct\_1~X5){\unicdcdcdhd}((v1\_finset\_1~X5){\unicdcdcdhd}(v3\_trees\_2~X5)))){\unicdbdjdcd}((r1\_msaterm~\\
X0~X1~X2~X4~X3~X5){\unicdbdjdcd}(k9\_msaterm~X0~X1~X2~X4~X3=k1\_funct\_1~X5~k1\_xboole\_0)))))))\end{array}$$
\end{theorem}
\end{document}
