\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{t12\_grcat\_1 (TMG8GAyTGvkZP2k5Tz8KyM5v9sX2NFET8hK)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_grcat\_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 $ u1\_struct\_0 : {{\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.
Let $ g1\_grcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_grcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_grcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_grcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v13\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v2\_grcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_grcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_grcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_grcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_grcat\_1~X0){\unicdcdcdhd}(l1\_grcat\_1~X0)){\unicdbdjdcd}(v13\_vectsp\_1~\\
(u3\_grcat\_1~X0)~(u1\_grcat\_1~X0)~(u2\_grcat\_1~X0))\end{array}
\label{hyp:ehjdpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_grcat\_1~X0){\unicdbdjdcd}((v1\_funct\_1~(u3\_grcat\_1~X0)){\unicdcdcdhd}((\\
v1\_funct\_2~(u3\_grcat\_1~X0)~(u1\_struct\_0~(u1\_grcat\_1~X0))~(u1\_struct\_0~\\
(u2\_grcat\_1~X0))){\unicdcdcdhd}(m1\_subset\_1~(u3\_grcat\_1~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~(u1\_grcat\_1~X0))~(u1\_struct\_0~(u2\_grcat\_1~\\
X0)))))))\end{array}
\label{hyp:egehpffhddpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}\\
((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l2\_algstr\_0~X0))))){\unicdcdcdhd}(\\
(\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~\\
X1){\unicdcdcdhd}(l2\_algstr\_0~X1)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_grcat\_1~X2~X0~X1){\unicdbdjdcd}\\
((v2\_grcat\_1~X2){\unicdcdcdhd}(l1\_grcat\_1~X2)))\end{array}
\label{hyp:egehpfngbdpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_grcat\_1}~{X0}})}{\unicdbdjdcd}{({{{k7\_grcat\_1}~{X0}}={{u1\_grcat\_1}~{X0}}})}}}\label{hyp:egjdpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v3\_rlvect\_1~\\
X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l2\_algstr\_0~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh \\
v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~\\
X1){\unicdcdcdhd}(l2\_algstr\_0~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v2\_grcat\_1~X2){\unicdcdcdhd}(l1\_grcat\_1~\\
X2)){\unicdbdjdcd}((m1\_grcat\_1~X2~X0~X1){\unicdbdjded}((k7\_grcat\_1~X2=X0){\unicdcdcdhd}(k8\_grcat\_1~\\
X2=X1)))))\end{array}
\label{hyp:egbdedpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_grcat\_1}~{X0}})}{\unicdbdjdcd}{({{{k8\_grcat\_1}~{X0}}={{u2\_grcat\_1}~{X0}}})}}}\label{hyp:egbdadpfhgchdgbgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdcdpfhgchdgbgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v3\_rlvect\_1~\\
X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l2\_algstr\_0~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh \\
v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~\\
X1){\unicdcdcdhd}(l2\_algstr\_0~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_grcat\_1~X2~X0~X1){\unicdbdjdcd}(\\
{\unicdcdaddd} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))){\unicdcdcdhd}((g1\_grcat\_1~(u1\_grcat\_1~\\
X2)~(u2\_grcat\_1~X2)~(u3\_grcat\_1~X2)=g1\_grcat\_1~X0~X1~X3){\unicdcdcdhd}(v13\_vectsp\_1~\\
X3~X0~X1)))))\end{array}$$
\end{theorem}
\end{document}
