\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{t62\_circtrm1 (TMS7A8AbCZrHb11rhLmrzNNes9E7GiRtkSU)}
\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 $ v4\_msafree2 : {{\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 $ m3\_msaterm : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v2\_msafree2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r8\_circtrm1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}$ be given.
Let $ m1\_dtconstr : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ k9\_trees\_9 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_facirc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k5\_facirc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k6\_trees\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_circtrm1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}}$ be given.
Let $ k1\_circtrm1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_circtrm1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_circtrm1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_circtrm1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ r7\_circtrm1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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}((v4\_msafree2~X1~X0){\unicdcdcdhd}\\
(l3\_msualg\_1~X1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m4\_msaterm~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m3\_msaterm~X3~X0~X2){\unicdbdjdcd}({\unicdcdadad} X4 .  ((\preoh v2\_struct\_0~X4){\unicdcdcdhd}((\preoh v11\_struct\_0~\\
X4){\unicdcdcdhd}((v2\_msafree2~X4){\unicdcdcdhd}(l1\_msualg\_1~X4)))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v4\_msualg\_1~\\
X5~X4){\unicdcdcdhd}((v4\_msafree2~X5~X4){\unicdcdcdhd}(l3\_msualg\_1~X5~X4))){\unicdbdjdcd}((r7\_circtrm1~\\
X0~X1~X2~X3~X4~X5){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_dtconstr~X6~(u1\_struct\_0~(k5\_msafree~\\
X0~X2))~(k5\_trees\_3~(u1\_struct\_0~(k5\_msafree~X0~X2)))~(k1\_msaterm~\\
X0~X2)){\unicdbdjdcd}(\preoh (X6 \in k9\_trees\_9~X3){\unicdcdcdhd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(u1\_struct\_0~\\
X4)){\unicdbdjdcd}(\preoh {\unicdcdadad} X8 .  (m1\_subset\_1~X8~(k4\_card\_3~(u3\_msualg\_1~X4~\\
X5))){\unicdbdjdcd}((r1\_facirc\_1~X4~X5~(k5\_facirc\_1~X4~X5~X8~(k2\_nat\_1~np\_\_1~\\
(k6\_trees\_1~(k9\_xtuple\_0~X6))))~X7){\unicdcdcdhd}({\unicdcdaddd} X9 .  (m2\_circtrm1~\\
X9~X0~X2~X1~X3~X4~X5){\unicdcdcdhd}({\unicdcdadad} X10 .  (m1\_subset\_1~X10~(k4\_card\_3~(u3\_msualg\_1~\\
(k1\_circtrm1~X0~X2~X3)~(k6\_circtrm1~X0~X2~X3~X1)))){\unicdbdjdcd}((X10=k3\_relat\_1~\\
X9~X8){\unicdbdjdcd}({\unicdcdadad} X11 .  (m1\_circtrm1~X11~X0~X2~X3~X1~X10){\unicdbdjdcd}(k1\_funct\_1~\\
(k5\_facirc\_1~X4~X5~X8~(k2\_nat\_1~np\_\_1~(k6\_trees\_1~(k9\_xtuple\_0~\\
X6))))~X7=k7\_circtrm1~X0~X1~X2~X6~X11))))))))))))))))\end{array}
\label{hyp:ehgdadpfdgjgchdgehchngbd}
\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}((v4\_msafree2~X1~X0){\unicdcdcdhd}\\
(l3\_msualg\_1~X1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m4\_msaterm~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m3\_msaterm~X3~X0~X2){\unicdbdjdcd}({\unicdcdadad} X4 .  ((\preoh v2\_struct\_0~X4){\unicdcdcdhd}((\preoh v11\_struct\_0~\\
X4){\unicdcdcdhd}((v2\_msafree2~X4){\unicdcdcdhd}(l1\_msualg\_1~X4)))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v4\_msualg\_1~\\
X5~X4){\unicdcdcdhd}((v4\_msafree2~X5~X4){\unicdcdcdhd}(l3\_msualg\_1~X5~X4))){\unicdbdjdcd}((r8\_circtrm1~\\
X0~X1~X2~X3~X4~X5){\unicdbdjdcd}(r7\_circtrm1~X0~X1~X2~X3~X4~X5)))))))\end{array}
\label{hyp:ehfdidpfdgjgchdgehchngbd}
\end{equation}
\begin{theorem}\label{thm:ehgdcdpfdgjgchdgehchngbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v4\_msualg\_1~X1~X0){\unicdcdcdhd}((v4\_msafree2~X1~X0){\unicdcdcdhd}\\
(l3\_msualg\_1~X1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m4\_msaterm~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m3\_msaterm~X3~X0~X2){\unicdbdjdcd}({\unicdcdadad} X4 .  ((\preoh v2\_struct\_0~X4){\unicdcdcdhd}((\preoh v11\_struct\_0~\\
X4){\unicdcdcdhd}((v2\_msafree2~X4){\unicdcdcdhd}(l1\_msualg\_1~X4)))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v4\_msualg\_1~\\
X5~X4){\unicdcdcdhd}((v4\_msafree2~X5~X4){\unicdcdcdhd}(l3\_msualg\_1~X5~X4))){\unicdbdjdcd}((r8\_circtrm1~\\
X0~X1~X2~X3~X4~X5){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_dtconstr~X6~(u1\_struct\_0~(k5\_msafree~\\
X0~X2))~(k5\_trees\_3~(u1\_struct\_0~(k5\_msafree~X0~X2)))~(k1\_msaterm~\\
X0~X2)){\unicdbdjdcd}(\preoh (X6 \in k9\_trees\_9~X3){\unicdcdcdhd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(u1\_struct\_0~\\
X4)){\unicdbdjdcd}(\preoh {\unicdcdadad} X8 .  (m1\_subset\_1~X8~(k4\_card\_3~(u3\_msualg\_1~X4~\\
X5))){\unicdbdjdcd}((r1\_facirc\_1~X4~X5~(k5\_facirc\_1~X4~X5~X8~(k2\_nat\_1~np\_\_1~\\
(k6\_trees\_1~(k9\_xtuple\_0~X6))))~X7){\unicdcdcdhd}({\unicdcdaddd} X9 .  (m2\_circtrm1~\\
X9~X0~X2~X1~X3~X4~X5){\unicdcdcdhd}({\unicdcdadad} X10 .  (m1\_subset\_1~X10~(k4\_card\_3~(u3\_msualg\_1~\\
(k1\_circtrm1~X0~X2~X3)~(k6\_circtrm1~X0~X2~X3~X1)))){\unicdbdjdcd}((X10=k3\_relat\_1~\\
X9~X8){\unicdbdjdcd}({\unicdcdadad} X11 .  (m1\_circtrm1~X11~X0~X2~X3~X1~X10){\unicdbdjdcd}(k1\_funct\_1~\\
(k5\_facirc\_1~X4~X5~X8~(k2\_nat\_1~np\_\_1~(k6\_trees\_1~(k9\_xtuple\_0~\\
X6))))~X7=k7\_circtrm1~X0~X1~X2~X6~X11))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
