\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{t68\_scmfsa\_2 (TMQnqPiDq59hxJttJXfs1Bj41MJKJBWAzmU)}
\maketitle
Let $ v1\_ami\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_scmfsa\_2 : {\iota}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k10\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_int\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k4\_numbers : {\iota}$ be given.
Let $ k18\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_int\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~(u1\_struct\_0~k1\_scmfsa\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X2){\unicdcdcdhd}((v5\_funct\_1~X2~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X2~(u1\_struct\_0~k1\_scmfsa\_2)))))){\unicdbdjdcd}((k1\_funct\_1~\\
(k2\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k10\_scmfsa\_2~X0~X1)~X2)~(k4\_struct\_0~\\
k1\_scmfsa\_2)=k4\_card\_1~(k5\_memstr\_0~np\_\_3~k1\_scmfsa\_2~X2)){\unicdcdcdhd}\\
(((X0{\unicdcdgdad}X1){\unicdbdjdcd}(k1\_funct\_1~(k2\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k10\_scmfsa\_2~\\
X0~X1)~X2)~X0=k5\_int\_1~(k1\_funct\_1~X2~X0)~(k1\_funct\_1~X2~X1))){\unicdcdcdhd}(\\
(k1\_funct\_1~(k2\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k10\_scmfsa\_2~X0~X1)~\\
X2)~X1=k6\_int\_1~(k1\_funct\_1~X2~X0)~(k1\_funct\_1~X2~X1)){\unicdcdcdhd}(({\unicdcdadad} X3 .  \\
((v1\_ami\_2~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
(\preoh (X3{\unicdcdgdad}X0){\unicdcdcdhd}((X3{\unicdcdgdad}X1){\unicdcdcdhd}(k1\_funct\_1~(k2\_extpro\_1~np\_\_3~k1\_scmfsa\_2~\\
(k10\_scmfsa\_2~X0~X1)~X2)~X3{\unicdcdgdad}k1\_funct\_1~X2~X3)))){\unicdcdcdhd}({\unicdcdadad} X3 .  (\\
m1\_scmfsa\_2~X3){\unicdbdjdcd}(r2\_relset\_1~k5\_numbers~k4\_numbers~(k18\_scmfsa\_2~\\
(k2\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k10\_scmfsa\_2~X0~X1)~X2)~X3)~(k18\_scmfsa\_2~\\
X2~X3)))))))))\end{array}
\label{hyp:ehgdhdpfdhdgngggdhbgpfcd}
\end{equation}
\begin{theorem}\label{thm:ehgdidpfdhdgngggdhbgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~(u1\_struct\_0~k1\_scmfsa\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_funct\_1~X1~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X1~(u1\_struct\_0~k1\_scmfsa\_2)))))){\unicdbdjdcd}((k1\_funct\_1~\\
(k2\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k10\_scmfsa\_2~X0~X0)~X1)~(k4\_struct\_0~\\
k1\_scmfsa\_2)=k4\_card\_1~(k5\_memstr\_0~np\_\_3~k1\_scmfsa\_2~X1)){\unicdcdcdhd}\\
((k1\_funct\_1~(k2\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k10\_scmfsa\_2~X0~\\
X0)~X1)~X0=k6\_int\_1~(k1\_funct\_1~X1~X0)~(k1\_funct\_1~X1~X0)){\unicdcdcdhd}(({\unicdcdadad} X2 .  \\
((v1\_ami\_2~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
((X2{\unicdcdgdad}X0){\unicdbdjdcd}(k1\_funct\_1~(k2\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k10\_scmfsa\_2~\\
X0~X0)~X1)~X2=k1\_funct\_1~X1~X2))){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_scmfsa\_2~X2){\unicdbdjdcd}\\
(r2\_relset\_1~k5\_numbers~k4\_numbers~(k18\_scmfsa\_2~(k2\_extpro\_1~\\
np\_\_3~k1\_scmfsa\_2~(k10\_scmfsa\_2~X0~X0)~X1)~X2)~(k18\_scmfsa\_2~X1~\\
X2)))))))\end{array}$$
\end{theorem}
\end{document}
