\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\_scmpds\_5 (TMRXGxu6DXsiECKd18poFBcHuGsjczkj5jj)}
\maketitle
Let $ v1\_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 $ k1\_scmpds\_2 : {\iota}$ 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\_\_2 : {\iota}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_scmpds\_4 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_compos\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_6 : {\iota}$ be given.
Let $ np\_\_14 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_funct\_1~X1~(k2\_memstr\_0~np\_\_2~k1\_scmpds\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X1~(u1\_struct\_0~k1\_scmpds\_2)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X2){\unicdcdcdhd}((v5\_funct\_1~X2~(k2\_memstr\_0~np\_\_2~k1\_scmpds\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X2~(u1\_struct\_0~k1\_scmpds\_2)))))){\unicdbdjdcd}((k6\_memstr\_0~\\
np\_\_2~k1\_scmpds\_2~X1=k6\_memstr\_0~np\_\_2~k1\_scmpds\_2~X2){\unicdbdjdcd}((k2\_compos\_0~\\
(u1\_compos\_1~k1\_scmpds\_2)~X0=np\_\_3){\unicdcdcdid}(k6\_memstr\_0~np\_\_2~k1\_scmpds\_2~\\
(k2\_extpro\_1~np\_\_2~k1\_scmpds\_2~X0~X1)=k6\_memstr\_0~np\_\_2~k1\_scmpds\_2~\\
(k2\_extpro\_1~np\_\_2~k1\_scmpds\_2~X0~X2))))))\end{array}
\label{hyp:ehddidpfdhdgngahegdhpffd}
\end{equation}
Assume the following.
\begin{equation}
{{{r1\_xxreal\_0}~{np\_\_3}}~{np\_\_6}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchddpfchgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdbdjdcd}((v4\_scmpds\_4~\\
X0){\unicdbdjded}((k2\_compos\_0~(u1\_compos\_1~k1\_scmpds\_2)~X0=np\_\_2){\unicdcdcdid}((k2\_compos\_0~\\
(u1\_compos\_1~k1\_scmpds\_2)~X0{\unicdcdgdad}np\_\_14){\unicdcdcdhd}(\preoh r1\_xxreal\_0~(k2\_compos\_0~\\
(u1\_compos\_1~k1\_scmpds\_2)~X0)~np\_\_6))))\end{array}
\label{hyp:egbdadpfdhdgngahegdhpfed}
\end{equation}
\begin{theorem}\label{thm:ehddjdpfdhdgngahegdhpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X0){\unicdcdcdhd}((v5\_funct\_1~X0~(k2\_memstr\_0~np\_\_2~k1\_scmpds\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X0~(u1\_struct\_0~k1\_scmpds\_2)))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_funct\_1~X1~(k2\_memstr\_0~np\_\_2~k1\_scmpds\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X1~(u1\_struct\_0~k1\_scmpds\_2)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v4\_scmpds\_4~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_compos\_1~k1\_scmpds\_2))){\unicdbdjdcd}\\
((k6\_memstr\_0~np\_\_2~k1\_scmpds\_2~X0=k6\_memstr\_0~np\_\_2~k1\_scmpds\_2~\\
X1){\unicdbdjdcd}(k6\_memstr\_0~np\_\_2~k1\_scmpds\_2~(k2\_extpro\_1~np\_\_2~k1\_scmpds\_2~\\
X2~X0)=k6\_memstr\_0~np\_\_2~k1\_scmpds\_2~(k2\_extpro\_1~np\_\_2~k1\_scmpds\_2~\\
X2~X1)))))\end{array}$$
\end{theorem}
\end{document}
