\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{t29\_c0sp2 (TMVGXdYZ5z3eFNB8sfCMHQ9T7fpoQiVMG8X)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_rlsub\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_c0sp2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_funcsdom : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_rlvect\_1 : {{\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 $ v1\_rlsub\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ g1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k10\_rsspace : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_rsspace : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_rsspace : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_c0sp2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k8\_funcsdom : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_funcsdom : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_funcsdom : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v5\_rlvect\_1~X0){\unicdcdcdhd}\\
((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~X0){\unicdcdcdhd}(l1\_rlvect\_1~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}((v1\_rlsub\_1~X1~X0){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}(m1\_rlsub\_1~(g1\_rlvect\_1~\\
X1~(k10\_rsspace~X0~X1)~(k8\_rsspace~X0~X1)~(k9\_rsspace~X0~X1))~X0))))\end{array}
\label{hyp:ehbdbdpfchdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k6\_c0sp2~X0)){\unicdcdcdhd}(v1\_rlsub\_1~(k6\_c0sp2~X0)~\\
(k10\_funcsdom~(u1\_struct\_0~X0))))\end{array}
\label{hyp:ggdgbdddpfdgaddhahcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k6\_c0sp2~X0)){\unicdcdcdhd}(m1\_subset\_1~(k6\_c0sp2~\\
X0)~(k1\_zfmisc\_1~(u1\_struct\_0~(k10\_funcsdom~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpflggdpfdgaddhahcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v2\_struct\_0~(k10\_funcsdom~X0)){\unicdcdcdhd}((v13\_algstr\_0~\\
(k10\_funcsdom~X0)){\unicdcdcdhd}((v1\_rlvect\_1~(k10\_funcsdom~X0)){\unicdcdcdhd}((v2\_rlvect\_1~\\
(k10\_funcsdom~X0)){\unicdcdcdhd}((v3\_rlvect\_1~(k10\_funcsdom~X0)){\unicdcdcdhd}((v4\_rlvect\_1~\\
(k10\_funcsdom~X0)){\unicdcdcdhd}((v5\_rlvect\_1~(k10\_funcsdom~X0)){\unicdcdcdhd}((v6\_rlvect\_1~\\
(k10\_funcsdom~X0)){\unicdcdcdhd}((v7\_rlvect\_1~(k10\_funcsdom~X0)){\unicdcdcdhd}((v8\_rlvect\_1~\\
(k10\_funcsdom~X0)){\unicdcdcdhd}(l1\_rlvect\_1~(k10\_funcsdom~X0)))))))))))\end{array}
\label{hyp:egehpflgbdadpfggfhogdgdhegpgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}(k7\_c0sp2~X0=g1\_rlvect\_1~(k6\_c0sp2~X0)~(k10\_rsspace~(k10\_funcsdom~\\
(u1\_struct\_0~X0))~(k6\_c0sp2~X0))~(k8\_rsspace~(k10\_funcsdom~(u1\_struct\_0~\\
X0))~(k6\_c0sp2~X0))~(k9\_rsspace~(k10\_funcsdom~(u1\_struct\_0~X0))~\\
(k6\_c0sp2~X0)))\end{array}
\label{hyp:eghdpfdgaddhahcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  k10\_funcsdom~X0=g1\_rlvect\_1~(k9\_funct\_2~X0~k1\_numbers)~\\
(k8\_funcsdom~X0)~(k5\_funcsdom~X0)~(k7\_funcsdom~X0)\end{array}
\label{hyp:eggdpfggfhogdgdhegpgng}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k8\_funcsdom}~{X0}}={{{{k8\_funcop\_1}~{k5\_numbers}}~{X0}}~{k6\_numbers}}}}\label{hyp:egedpfggfhogdgdhegpgng}
\end{equation}
\begin{theorem}\label{thm:ehcdjdpfdgaddhahcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}(m1\_rlsub\_1~(k7\_c0sp2~X0)~(k10\_funcsdom~(u1\_struct\_0~X0)))\end{array}$$
\end{theorem}
\end{document}
