\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{t29\_sublemma (TMKBKw9EVMhuNPFRREiVMHJQrxjUUtbEHzo)}
\maketitle
Let $ m1\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_sublemma : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k16\_substut1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v3\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_sublemma : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_sublemma : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k8\_sublemma : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k31\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k24\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k22\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v7\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k38\_substut1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k2\_zfmisc\_1~\\
(k16\_substut1~X0)~(k3\_qc\_lang1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_substut1~\\
X2~X0~X1){\unicdbdjdcd}((v3\_substut1~X1~X0){\unicdbdjdcd}(k31\_substut1~X0~(k24\_substut1~\\
X0~X1~X2)=k22\_substut1~X0~X1))))\end{array}
\label{hyp:ehcdbdpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k2\_zfmisc\_1~\\
(k16\_substut1~X0)~(k3\_qc\_lang1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_substut1~\\
X2~X0~X1){\unicdbdjdcd}((v3\_substut1~X1~X0){\unicdbdjdcd}(v7\_substut1~(k24\_substut1~X0~X1~\\
X2)~X0))))\end{array}
\label{hyp:ehbdedpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}((v1\_sublemma~X1~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k2\_zfmisc\_1~(k16\_substut1~X0)~(k3\_qc\_lang1~X0))))){\unicdbdjdcd}\\
(k8\_sublemma~X0~X1=k1\_xtuple\_0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfdhfhcgmgfgngngbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k2\_zfmisc\_1~\\
(k16\_substut1~X0)~(k3\_qc\_lang1~X0)))){\unicdbdjdcd}(k22\_substut1~X0~X1=k1\_xtuple\_0~\\
X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdcdpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}(((v1\_sublemma~\\
X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k2\_zfmisc\_1~(k16\_substut1~X0)~(k3\_qc\_lang1~\\
X0)))){\unicdcdcdhd}(m1\_substut1~X2~X0~X1))){\unicdbdjdcd}(m2\_subset\_1~(k9\_sublemma~X0~\\
X1~X2)~(k16\_substut1~X0)~(k38\_substut1~X0))\end{array}
\label{hyp:egehpflgjdpfdhfhcgmgfgngngbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~X1~(k16\_substut1~\\
X0)~(k38\_substut1~X0)){\unicdbdjdcd}((v7\_substut1~X1~X0){\unicdbdjdcd}(k10\_sublemma~X0~\\
X1=k31\_substut1~X0~X1)))\end{array}
\label{hyp:eggdpfdhfhcgmgfgngngbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_sublemma~X1~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k2\_zfmisc\_1~(k16\_substut1~X0)~(k3\_qc\_lang1~X0)))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_substut1~X2~X0~X1){\unicdbdjdcd}((v3\_substut1~X1~X0){\unicdbdjdcd}(k9\_sublemma~\\
X0~X1~X2=k24\_substut1~X0~X1~X2))))\end{array}
\label{hyp:egfdpfdhfhcgmgfgngngbg}
\end{equation}
\begin{theorem}\label{thm:ehcdjdpfdhfhcgmgfgngngbg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_sublemma~X1~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k2\_zfmisc\_1~(k16\_substut1~X0)~(k3\_qc\_lang1~X0)))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_substut1~X2~X0~X1){\unicdbdjdcd}((v3\_substut1~X1~X0){\unicdbdjdcd}(k10\_sublemma~\\
X0~(k9\_sublemma~X0~X1~X2)=k8\_sublemma~X0~X1))))\end{array}$$
\end{theorem}
\end{document}
