\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{t48\_aofa\_000 (TMTZSJRTByksWckz5eu6WRho46qJRMz9fnC)}
\maketitle
Let $ v4\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_aofa\_000 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_pua2mss1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_4 : {\iota}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_unialg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_margrel1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_margrel1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k19\_margrel1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k18\_margrel1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v8\_comput\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{\preoh{{({{X0} \in {X1}})}}}{\unicdcdcdhd}{({{v1\_xboole\_0}~{X1}})}}}}\label{hyp:ehhdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v2\_margrel1~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_finseq\_2~X0)~X0))))){\unicdbdjdcd}(((v3\_margrel1~\\
X1~X0){\unicdcdcdhd}(\preoh v1\_xboole\_0~X1)){\unicdbdjded}(k1\_relset\_1~(k3\_finseq\_2~X0)~X1=k4\_finseq\_2~\\
(k19\_margrel1~X1)~X0))\end{array}
\label{hyp:ehcdcdpfdgpgngahfhehpfbd}
\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 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v2\_margrel1~X0))){\unicdbdjdcd}\\
(k19\_margrel1~X0=k18\_margrel1~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdjdpfngbgchhgchfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_unialg\_1~X0){\unicdbdjdcd}(m2\_finseq\_1~(u1\_unialg\_1~X0)~(k4\_partfun1~\\
(k3\_finseq\_2~(u1\_struct\_0~X0))~(u1\_struct\_0~X0)))\end{array}
\label{hyp:egehpffhbdpffhogjgbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m2\_finseq\_1~X1~X0){\unicdbdjdcd}((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_finseq\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
X0)))))\end{array}
\label{hyp:egehpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))){\unicdbdjdcd}\\
(m1\_subset\_1~(k4\_finseq\_1~X0)~(k1\_zfmisc\_1~k5\_numbers))\end{array}
\label{hyp:egehpflgedpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v2\_margrel1~X1)){\unicdbdjdcd}((\\
v8\_comput\_1~X1~X0){\unicdbdjded}(k18\_margrel1~X1=X0))\end{array}
\label{hyp:egcdbdpfdgpgngahfhehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_subset\_1~X1~k5\_numbers~(k4\_finseq\_1~(u1\_unialg\_1~X0))){\unicdbdjdcd}(\\
k2\_pua2mss1~X0~X1=k1\_funct\_1~(u1\_unialg\_1~X0)~X1))\end{array}
\label{hyp:egbdpfahfhbgcdngdhdhbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{{k1\_funct\_7}~{X0}}~{X1}}={X0}})}}}}\label{hyp:egbdpfggfhogdgehpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_unialg\_1~X0)){\unicdbdjdcd}((v6\_aofa\_000~\\
X0){\unicdbdjded}((np\_\_4 \in k4\_finseq\_1~(u1\_unialg\_1~X0)){\unicdcdcdhd}((\preoh v1\_xboole\_0~(\\
k1\_funct\_1~(u1\_unialg\_1~X0)~np\_\_4)){\unicdcdcdhd}((v1\_funct\_1~(k1\_funct\_1~\\
(u1\_unialg\_1~X0)~np\_\_4)){\unicdcdcdhd}((v2\_margrel1~(k1\_funct\_1~(u1\_unialg\_1~\\
X0)~np\_\_4)){\unicdcdcdhd}((v3\_margrel1~(k1\_funct\_1~(u1\_unialg\_1~X0)~np\_\_4)~\\
(u1\_struct\_0~X0)){\unicdcdcdhd}((v8\_comput\_1~(k1\_funct\_1~(u1\_unialg\_1~X0)~\\
np\_\_4)~np\_\_2){\unicdcdcdhd}(m1\_subset\_1~(k1\_funct\_1~(u1\_unialg\_1~X0)~np\_\_4)~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_finseq\_2~(u1\_struct\_0~X0))~(u1\_struct\_0~\\
X0)))))))))))\end{array}
\label{hyp:egbdddpfbgpgggbgpfadadad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_unialg\_1}~{X0}})}{\unicdbdjdcd}{({{({{v4\_unialg\_1}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v2\_struct\_0}~{X0}}}})}})}}}\label{hyp:dgdgcdpfahfhbgcdngdhdhbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_xboole\_0~X1))\end{array}
\label{hyp:dgdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v1\_relat\_1~X2)\end{array}
\label{hyp:dgdgbdpfchfgmgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedidpfbgpgggbgpfadadad}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v4\_unialg\_1~X0){\unicdcdcdhd}((v6\_aofa\_000~X0){\unicdcdcdhd}(l1\_unialg\_1~\\
X0))){\unicdbdjdcd}(k1\_relset\_1~(k3\_finseq\_2~(u1\_struct\_0~X0))~(k2\_pua2mss1~\\
X0~(k1\_funct\_7~np\_\_4~(k4\_finseq\_1~(u1\_unialg\_1~X0))))=k4\_finseq\_2~\\
np\_\_2~(u1\_struct\_0~X0))\end{array}$$
\end{theorem}
\end{document}
