\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{t37\_polyform (TMdzkF4bqbj9wo9WmvKrhEDd1ts6p8a4dtE)}
\maketitle
Let $ v2\_polyform : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_polyform : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_polyform : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_polyform : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_int\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_polyform : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_polyform : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_bspace : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_bspace : {\iota}$ be given.
Let $ k7\_bspace : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k7\_bspace~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k7\_bspace~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~X0){\unicdbdjdcd}(k3\_bspace~(k3\_rlvect\_1~(k7\_bspace~\\
X0)~X1~X2)~X3=k3\_rlvect\_1~k2\_bspace~(k3\_bspace~X1~X3)~(k3\_bspace~\\
X2~X3))))\end{array}
\label{hyp:ehddcdpfcgdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_polyform~X0){\unicdcdcdhd}((v3\_polyform~X0){\unicdcdcdhd}((v4\_polyform~\\
X0){\unicdcdcdhd}(l1\_polyform~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}(k17\_polyform~\\
X0~X1=k7\_bspace~(k8\_polyform~X0~X1)))\end{array}
\label{hyp:egbdedpfahpgmgjhggpgchng}
\end{equation}
\begin{theorem}\label{thm:ehddhdpfahpgmgjhggpgchng}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_polyform~X0){\unicdcdcdhd}((v3\_polyform~X0){\unicdcdcdhd}((v4\_polyform~\\
X0){\unicdcdcdhd}(l1\_polyform~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~(k17\_polyform~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~(k17\_polyform~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(k8\_polyform~X0~X1)){\unicdbdjdcd}(k3\_bspace~(k3\_rlvect\_1~\\
(k17\_polyform~X0~X1)~X2~X3)~X4=k3\_rlvect\_1~k2\_bspace~(k3\_bspace~\\
X2~X4)~(k3\_bspace~X3~X4))))))\end{array}$$
\end{theorem}
\end{document}
