\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{t22\_midsp\_3 (TMYWYcRcj9PoKjZd4aFEgahE5GjaYeqUVvS)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ m2\_midsp\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v4\_midsp\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_midsp\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_midsp\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k9\_midsp\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_midsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_midsp\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ v2\_midsp\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}((v2\_midsp\_1~X1){\unicdcdcdhd}(l1\_midsp\_3~X1~(k2\_nat\_1~X0~np\_\_2)))){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((v4\_midsp\_2~X2~X1){\unicdcdcdhd}(l1\_midsp\_2~X2~X1)){\unicdbdjdcd}((v2\_midsp\_3~\\
X1~X0){\unicdbdjded}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m2\_finseq\_2~X5~\\
(u1\_struct\_0~(u1\_midsp\_2~X1~X2))~(k4\_finseq\_2~(k2\_nat\_1~X0~np\_\_1)~\\
(u1\_struct\_0~(u1\_midsp\_2~X1~X2)))){\unicdbdjdcd}(k9\_midsp\_3~X0~X1~X2~X3~X5=k9\_midsp\_3~\\
X0~X1~X2~X4~X5)))))))\end{array}
\label{hyp:ehbdjdpfngjgegdhahpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_midsp\_3~\\
X1~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_midsp\_1~X1){\unicdcdcdhd}(l1\_midsp\_3~X1~(k2\_nat\_1~\\
X0~np\_\_2)))))\end{array}
\label{hyp:egehpfngcdpfngjgegdhahpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}((v2\_midsp\_1~X1){\unicdcdcdhd}(l1\_midsp\_3~X1~(k2\_nat\_1~X0~np\_\_2)))){\unicdbdjdcd}(\\
(m2\_midsp\_3~X1~X0){\unicdbdjded}(v2\_midsp\_3~X1~X0)))\end{array}
\label{hyp:egbdbdpfngjgegdhahpfdd}
\end{equation}
\begin{theorem}\label{thm:ehcdcdpfngjgegdhahpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_midsp\_3~\\
X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v4\_midsp\_2~X4~\\
X1){\unicdcdcdhd}(l1\_midsp\_2~X4~X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m2\_finseq\_2~X5~(u1\_struct\_0~\\
(u1\_midsp\_2~X1~X4))~(k4\_finseq\_2~(k2\_nat\_1~X0~np\_\_1)~(u1\_struct\_0~\\
(u1\_midsp\_2~X1~X4)))){\unicdbdjdcd}(k9\_midsp\_3~X0~X1~X4~X2~X5=k9\_midsp\_3~X0~X1~\\
X4~X3~X5))))))\end{array}$$
\end{theorem}
\end{document}
