\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{t32\_rlvect\_4 (TMHN7xcbUBHNugpT59p3zDLhA2zBF63r5Xf)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v1\_rlvect\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k8\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v13\_algstr\_0~\\
X2){\unicdcdcdhd}((v2\_rlvect\_1~X2){\unicdcdcdhd}((v3\_rlvect\_1~X2){\unicdcdcdhd}((v4\_rlvect\_1~X2){\unicdcdcdhd}\\
((v5\_rlvect\_1~X2){\unicdcdcdhd}((v6\_rlvect\_1~X2){\unicdcdcdhd}((v7\_rlvect\_1~X2){\unicdcdcdhd}((v8\_rlvect\_1~\\
X2){\unicdcdcdhd}(l1\_rlvect\_1~X2)))))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(\\
u1\_struct\_0~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X2)){\unicdbdjdcd}\\
(\preoh (X0{\unicdcdgdad}X1){\unicdcdcdhd}(v1\_rlvect\_3~(k8\_domain\_1~(u1\_struct\_0~X2)~(k1\_rlvect\_1~\\
X2~X3~X0)~(k1\_rlvect\_1~X2~X3~X1)~X4)~X2))))))\end{array}
\label{hyp:ehddbdpfchmgghfgdgehpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_rlvect\_1~X0)){\unicdbdjdcd}((v8\_rlvect\_1~\\
X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k1\_rlvect\_1~\\
X0~X1~np\_\_1=X1)))\end{array}
\label{hyp:egidpfchmgghfgdgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddcdpfchmgghfgdgehpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}\\
((v4\_rlvect\_1~X1){\unicdcdcdhd}((v5\_rlvect\_1~X1){\unicdcdcdhd}((v6\_rlvect\_1~X1){\unicdcdcdhd}((v7\_rlvect\_1~\\
X1){\unicdcdcdhd}((v8\_rlvect\_1~X1){\unicdcdcdhd}(l1\_rlvect\_1~X1)))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X1)){\unicdbdjdcd}(\preoh (X0{\unicdcdgdad}np\_\_1){\unicdcdcdhd}(v1\_rlvect\_3~(k8\_domain\_1~(\\
u1\_struct\_0~X1)~X2~(k1\_rlvect\_1~X1~X2~X0)~X3)~X1)))))\end{array}$$
\end{theorem}
\end{document}
