\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{t3\_lpspace1 (TMNVChx3Wt219nWQ5U8YqnRtV5qtRoGR2V9)}
\maketitle
Let $ v2\_struct\_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 $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_ideal\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_lpspace1 : {{\iota}{\unicdbdjdcd}{{\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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ g1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_funct\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_ideal\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_lpspace1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k1\_realset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ u1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_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 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~(u1\_struct\_0~\\
X0)~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k2\_zfmisc\_1~\\
X1~X1)~X1){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
X1~X1)~X1))))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~(\\
k2\_zfmisc\_1~k1\_numbers~X1)~X1){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(\\
k2\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~X1)~X1))))){\unicdbdjdcd}(((X2=k4\_struct\_0~\\
X0){\unicdcdcdhd}((X3=k1\_realset1~(u1\_algstr\_0~X0)~X1){\unicdcdcdhd}(X4=k2\_partfun1~(\\
k2\_zfmisc\_1~k1\_numbers~(u1\_struct\_0~X0))~(u1\_struct\_0~X0)~(u1\_rlvect\_1~\\
X0)~(k2\_zfmisc\_1~k1\_numbers~X1)))){\unicdbdjdcd}((v2\_rlvect\_1~(g1\_rlvect\_1~\\
X1~X2~X3~X4)){\unicdcdcdhd}((v3\_rlvect\_1~(g1\_rlvect\_1~X1~X2~X3~X4)){\unicdcdcdhd}((v4\_rlvect\_1~\\
(g1\_rlvect\_1~X1~X2~X3~X4)){\unicdcdcdhd}((v5\_rlvect\_1~(g1\_rlvect\_1~X1~X2~X3~X4)){\unicdcdcdhd}\\
((v6\_rlvect\_1~(g1\_rlvect\_1~X1~X2~X3~X4)){\unicdcdcdhd}((v7\_rlvect\_1~(g1\_rlvect\_1~\\
X1~X2~X3~X4)){\unicdcdcdhd}(v8\_rlvect\_1~(g1\_rlvect\_1~X1~X2~X3~X4)))))))))))))\end{array}
\label{hyp:ehcdpfmgahdhahbgdgfgbd}
\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}
{{\unicdcdadad} X0 .  {{({{l1\_rlvect\_1}~{X0}})}{\unicdbdjdcd}{({{l2\_algstr\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfchmgghfgdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_rlvect\_1~X0)){\unicdcdcdhd}\\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_lpspace1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0)))))){\unicdbdjdcd}((v1\_funct\_1~(k1\_lpspace1~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~\\
(k1\_lpspace1~X0~X1)~(k2\_zfmisc\_1~k1\_numbers~X1)~X1){\unicdcdcdhd}(m1\_subset\_1~\\
(k1\_lpspace1~X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~\\
X1)~X1)))))\end{array}
\label{hyp:egehpflgbdpfmgahdhahbgdgfgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_algstr\_0~X0)){\unicdcdcdhd}\\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_ideal\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0)))))){\unicdbdjdcd}((v1\_funct\_1~(k1\_ideal\_1~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~\\
(k1\_ideal\_1~X0~X1)~(k2\_zfmisc\_1~X1~X1)~X1){\unicdcdcdhd}(m1\_subset\_1~(k1\_ideal\_1~\\
X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X1~X1)~X1)))))\end{array}
\label{hyp:egehpflgbdpfjgegfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_algstr\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_ideal\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))))){\unicdbdjdcd}(k1\_ideal\_1~X0~X1=k1\_realset1~(u1\_algstr\_0~\\
X0)~X1))\end{array}
\label{hyp:egfdpfjgegfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_rlvect\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_lpspace1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))))){\unicdbdjdcd}(k1\_lpspace1~X0~X1=k2\_partfun1~(k2\_zfmisc\_1~\\
k1\_numbers~(u1\_struct\_0~X0))~(u1\_struct\_0~X0)~(u1\_rlvect\_1~X0)~\\
(k2\_zfmisc\_1~k1\_numbers~X1)))\end{array}
\label{hyp:egcdpfmgahdhahbgdgfgbd}
\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 .  (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}
\begin{theorem}\label{thm:ehddpfmgahdhahbgdgfgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~\\
X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v5\_rlvect\_1~X0){\unicdcdcdhd}((v6\_rlvect\_1~X0){\unicdcdcdhd}\\
((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~X0){\unicdcdcdhd}(l1\_rlvect\_1~X0))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_ideal\_1~X1~X0){\unicdcdcdhd}((v1\_lpspace1~\\
X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))))){\unicdbdjdcd}((\\
k4\_struct\_0~X0 \in X1){\unicdbdjdcd}((v2\_rlvect\_1~(g1\_rlvect\_1~X1~(k1\_funct\_7~\\
(k4\_struct\_0~X0)~X1)~(k1\_ideal\_1~X0~X1)~(k1\_lpspace1~X0~X1))){\unicdcdcdhd}(\\
(v3\_rlvect\_1~(g1\_rlvect\_1~X1~(k1\_funct\_7~(k4\_struct\_0~X0)~X1)~\\
(k1\_ideal\_1~X0~X1)~(k1\_lpspace1~X0~X1))){\unicdcdcdhd}((v4\_rlvect\_1~(g1\_rlvect\_1~\\
X1~(k1\_funct\_7~(k4\_struct\_0~X0)~X1)~(k1\_ideal\_1~X0~X1)~(k1\_lpspace1~\\
X0~X1))){\unicdcdcdhd}((v5\_rlvect\_1~(g1\_rlvect\_1~X1~(k1\_funct\_7~(k4\_struct\_0~\\
X0)~X1)~(k1\_ideal\_1~X0~X1)~(k1\_lpspace1~X0~X1))){\unicdcdcdhd}((v6\_rlvect\_1~\\
(g1\_rlvect\_1~X1~(k1\_funct\_7~(k4\_struct\_0~X0)~X1)~(k1\_ideal\_1~X0~\\
X1)~(k1\_lpspace1~X0~X1))){\unicdcdcdhd}((v7\_rlvect\_1~(g1\_rlvect\_1~X1~(k1\_funct\_7~\\
(k4\_struct\_0~X0)~X1)~(k1\_ideal\_1~X0~X1)~(k1\_lpspace1~X0~X1))){\unicdcdcdhd}(\\
v8\_rlvect\_1~(g1\_rlvect\_1~X1~(k1\_funct\_7~(k4\_struct\_0~X0)~X1)~(\\
k1\_ideal\_1~X0~X1)~(k1\_lpspace1~X0~X1)))))))))))\end{array}$$
\end{theorem}
\end{document}
