\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{t10\_gr\_cy\_3 (TMGpeq3A2ZqigGLkgXdu7sHSLyoXTzK1kaQ)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_int\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_gr\_cy\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_gr\_cy\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((v2\_gr\_cy\_3~X0){\unicdbdjded}((v7\_ordinal1~\\
(k2\_nat\_1~(k4\_nat\_1~np\_\_2~X0)~np\_\_1)){\unicdcdcdhd}(v1\_int\_2~(k2\_nat\_1~(k4\_nat\_1~\\
np\_\_2~X0)~np\_\_1))))\end{array}
\label{hyp:egcdpfhgchpfdgjhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((v1\_gr\_cy\_3~X0){\unicdbdjded}({\unicdcdaddd} X1 .  ((\\
v7\_ordinal1~X1){\unicdcdcdhd}(v1\_int\_2~X1)){\unicdcdcdhd}(k2\_nat\_1~(k4\_nat\_1~np\_\_2~X1)~\\
np\_\_1=X0)))\end{array}
\label{hyp:egbdpfhgchpfdgjhpfdd}
\end{equation}
\begin{theorem}\label{thm:ehbdadpfhgchpfdgjhpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}((v1\_int\_2~X0){\unicdcdcdhd}(v1\_gr\_cy\_3~X0))){\unicdbdjdcd}\\
({\unicdcdaddd} X1 .  ((v7\_ordinal1~X1){\unicdcdcdhd}((v1\_int\_2~X1){\unicdcdcdhd}(v2\_gr\_cy\_3~X1))){\unicdcdcdhd}\\
(X0=k2\_nat\_1~(k4\_nat\_1~np\_\_2~X1)~np\_\_1))\end{array}$$
\end{theorem}
\end{document}
