\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{t37\_scmfsa\_2 (TMVFMatPSWQXVRXFHsiVZEcudnGVLNJiN1z)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_scmfsa\_2 : {\iota}$ be given.
Let $ k2\_compos\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_8 : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_ami\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k13\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_ami\_3 : {\iota}$ be given.
Let $ k9\_ami\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_scmfsa\_2 : {\iota}$ be given.
Let $ k2\_scm\_inst : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_compos\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_ami\_2 : {\iota}$ be given.
Let $ l1\_compos\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_compos\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_compos\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_compos\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdbdjdcd}((r1\_xxreal\_0~\\
(k2\_compos\_0~(u1\_compos\_1~k1\_scmfsa\_2)~X0)~np\_\_8){\unicdbdjdcd}(m1\_subset\_1~\\
X0~(u1\_compos\_1~k1\_ami\_3)))\end{array}
\label{hyp:ehbdfdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_ami\_3)){\unicdbdjdcd}(\preoh (k2\_compos\_0~\\
(u1\_compos\_1~k1\_ami\_3)~X0=np\_\_8){\unicdcdcdhd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~\\
k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_ami\_2~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~\\
k1\_ami\_3))){\unicdbdjdcd}(X0{\unicdcdgdad}k9\_ami\_3~X1~X2))))\end{array}
\label{hyp:ehbdfdpfbgngjgpffd}
\end{equation}
Assume the following.
\begin{equation}
{{{r1\_xxreal\_0}~{np\_\_8}}~{np\_\_8}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchidpfchid}
\end{equation}
Assume the following.
\begin{equation}
{{k2\_scmfsa\_2}={k2\_scm\_inst}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_compos\_0~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~X0)){\unicdbdjdcd}(k2\_compos\_0~X0~X1=k4\_xtuple\_0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfdgpgngahpgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
{{k2\_ami\_2}={k2\_scm\_inst}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfbgngjgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_compos\_1~X0){\unicdbdjdcd}((v1\_compos\_0~(u1\_compos\_1~X0)){\unicdcdcdhd}\\
((v2\_compos\_0~(u1\_compos\_1~X0)){\unicdcdcdhd}((v3\_compos\_0~(u1\_compos\_1~\\
X0)){\unicdcdcdhd}(v5\_compos\_0~(u1\_compos\_1~X0)))))\end{array}
\label{hyp:egehpffhbdpfdgpgngahpgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (l1\_extpro\_1~X1~X0){\unicdbdjdcd}((l1\_memstr\_0~X1~X0){\unicdcdcdhd}\\
(l1\_compos\_1~X1))\end{array}
\label{hyp:egehpfmgbdpffgihehahchpgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k2\_scmfsa\_2}}~{({{k1\_zfmisc\_1}~{({{u1\_struct\_0}~{k1\_scmfsa\_2}})}})}}\label{hyp:egehpflgcdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{({{{v1\_extpro\_1}~{k1\_scmfsa\_2}}~{np\_\_3}})}{\unicdcdcdhd}{({{{l1\_extpro\_1}~{k1\_scmfsa\_2}}~{np\_\_3}})}}\label{hyp:egehpflgbdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{({{{v1\_extpro\_1}~{k1\_ami\_3}}~{np\_\_2}})}{\unicdcdcdhd}{({{{l1\_extpro\_1}~{k1\_ami\_3}}~{np\_\_2}})}}\label{hyp:egehpflgbdpfbgngjgpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k4\_xtuple\_0}~{X0}}={{k1\_xtuple\_0}~{({{k1\_xtuple\_0}~{X0}})}}}}\label{hyp:eggdpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_ami\_2}~{X0}})}{\unicdbdjded}{({{X0} \in {k2\_ami\_2}})}}}\label{hyp:egbdgdpfbgngjgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_ami\_2~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdbdjdcd}((X2=k13\_scmfsa\_2~\\
X0~X1){\unicdbdjded}({\unicdcdaddd} X3 .  ((v1\_ami\_2~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(u1\_struct\_0~\\
k1\_ami\_3))){\unicdcdcdhd}((X1=X3){\unicdcdcdhd}(X2=k9\_ami\_3~X0~X3))))))\end{array}
\label{hyp:egbdfdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v5\_compos\_0}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{X0}}}})}}}\label{hyp:dgdgcdpfdgpgngahpgdhpfad}
\end{equation}
\begin{theorem}\label{thm:ehddhdpfdhdgngggdhbgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdbdjdcd}(\preoh (k2\_compos\_0~\\
(u1\_compos\_1~k1\_scmfsa\_2)~X0=np\_\_8){\unicdcdcdhd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_ami\_2~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~\\
k1\_scmfsa\_2))){\unicdbdjdcd}(X0{\unicdcdgdad}k13\_scmfsa\_2~X1~X2))))\end{array}$$
\end{theorem}
\end{document}
