\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{t19\_latsubgr (TMRVuyY5nhbvrtL5pUv21a6eVgGzZ61LL4q)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v15\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_group\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_latsubgr : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_group\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ k1\_group\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_setfam\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_group\_2~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_group\_2~X2~X0){\unicdbdjdcd}(u1\_struct\_0~(k10\_group\_2~X0~X1~X2)=k3\_xboole\_0~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~X2))))\end{array}
\label{hyp:ehbdpfmgbgehdhfhcghgch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}((v1\_funct\_1~(k1\_latsubgr~X0)){\unicdcdcdhd}((v1\_funct\_2~\\
(k1\_latsubgr~X0)~(k1\_group\_3~X0)~(k9\_setfam\_1~(u1\_struct\_0~X0))){\unicdcdcdhd}\\
(m1\_subset\_1~(k1\_latsubgr~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_group\_3~\\
X0)~(k9\_setfam\_1~(u1\_struct\_0~X0)))))))\end{array}
\label{hyp:egehpflgbdpfmgbgehdhfhcghgch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~\\
X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdcdcdhd}((m1\_group\_2~X1~X0){\unicdcdcdhd}\\
(m1\_group\_2~X2~X0))){\unicdbdjdcd}((v15\_algstr\_0~(k10\_group\_2~X0~X1~X2)){\unicdcdcdhd}(\\
m1\_group\_2~(k10\_group\_2~X0~X1~X2)~X0))\end{array}
\label{hyp:egehpflgbdadpfhgchpgfhahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~(k1\_group\_3~X0)~(k9\_setfam\_1~(u1\_struct\_0~X0))){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_group\_3~X0)~(k9\_setfam\_1~(u1\_struct\_0~\\
X0))))))){\unicdbdjdcd}((X1=k1\_latsubgr~X0){\unicdbdjded}({\unicdcdadad} X2 .  ((v15\_algstr\_0~\\
X2){\unicdcdcdhd}(m1\_group\_2~X2~X0)){\unicdbdjdcd}(k1\_funct\_1~X1~X2=u1\_struct\_0~X2))))\end{array}
\label{hyp:egbdpfmgbgehdhfhcghgch}
\end{equation}
\begin{theorem}\label{thm:ehbdjdpfmgbgehdhfhcghgch}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v15\_algstr\_0~X1){\unicdcdcdhd}(m1\_group\_2~\\
X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v15\_algstr\_0~X2){\unicdcdcdhd}(m1\_group\_2~X2~X0)){\unicdbdjdcd}(\\
k1\_funct\_1~(k1\_latsubgr~X0)~(k10\_group\_2~X0~X1~X2)=k3\_xboole\_0~\\
(k1\_funct\_1~(k1\_latsubgr~X0)~X1)~(k1\_funct\_1~(k1\_latsubgr~X0)~\\
X2))))\end{array}$$
\end{theorem}
\end{document}
