\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{t39\_sublemma (TMNMnFghuDnYwWJrj7EV7C6T4YiFopvy2pY)}
\maketitle
Let $ m1\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k16\_substut1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k38\_substut1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k7\_sublemma : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v3\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k11\_cqc\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_sublemma : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k35\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k32\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_sublemma : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k21\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k15\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k22\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k18\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k24\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k23\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k22\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k19\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_substut1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k34\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k33\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_cqc\_lang : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_sublemma : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_qc\_lang3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k13\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~X1~(k2\_qc\_lang1~\\
X0)~(k3\_qc\_lang1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k9\_qc\_lang1~\\
X0)){\unicdbdjdcd}((k21\_qc\_lang1~X0~(k15\_qc\_lang1~X0~X1~X2)=X1){\unicdcdcdhd}(k22\_qc\_lang1~\\
X0~(k15\_qc\_lang1~X0~X1~X2)=X2))))\end{array}
\label{hyp:ehhdpfbhdgpfmgbgoghgcd}
\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}((k18\_substut1~X0~(k24\_substut1~\\
X0~X1~X2)=k15\_qc\_lang1~X0~(k23\_substut1~X0~X1)~(k18\_substut1~X0~\\
(k22\_substut1~X0~X1))){\unicdcdcdhd}(k19\_substut1~X0~(k24\_substut1~X0~X1~X2)=\\
X2)))))\end{array}
\label{hyp:ehcdgdpfdhfhcgmgfgngngbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~(k38\_substut1~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k3\_qc\_lang1~X0)))){\unicdbdjdcd}(k7\_sublemma~\\
X0~X1~X2=k4\_tarski~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfdhfhcgmgfgngngbg}
\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~\\
(k9\_qc\_lang1~X0)~(k1\_substut1~X0)))){\unicdbdjdcd}(k34\_substut1~X0~X1=k2\_xtuple\_0~\\
X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddedpfdhfhcgdhehfhehbd}
\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~\\
(k9\_qc\_lang1~X0)~(k1\_substut1~X0)))){\unicdbdjdcd}(k33\_substut1~X0~X1=k1\_xtuple\_0~\\
X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddddpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k38\_substut1~\\
X0))){\unicdbdjdcd}(k2\_sublemma~X0~X1=k1\_xtuple\_0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfdhfhcgmgfgngngbg}
\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}(k23\_substut1~X0~X1=k2\_xtuple\_0~\\
X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdddpfdhfhcgdhehfhehbd}
\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 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k16\_substut1~\\
X0))){\unicdbdjdcd}(k19\_substut1~X0~X1=k2\_xtuple\_0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdjdpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k16\_substut1~\\
X0))){\unicdbdjdcd}(k18\_substut1~X0~X1=k1\_xtuple\_0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdidpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~(k3\_qc\_lang1~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k3\_cqc\_lang~X0)))){\unicdbdjdcd}(k11\_cqc\_lang~\\
X0~X1~X2=k15\_qc\_lang1~X0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdbdpfdgbhdgpfmgbgoghg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{k2\_xtuple\_0}~{({{{k4\_tarski}~{X0}}~{X1}})}}={X1}}}}\label{hyp:chegcdpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{k1\_xtuple\_0}~{({{{k4\_tarski}~{X0}}~{X1}})}}={X0}}}}\label{hyp:chegbdpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{m1\_qc\_lang1}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{({{k38\_substut1}~{X0}})}}}})}}}\label{hyp:ggdghdpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{m1\_qc\_lang1}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{({{k3\_qc\_lang1}~{X0}})}}}})}}}\label{hyp:ggdgddpfbhdgpfmgbgoghgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{m1\_qc\_lang1}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{({{k3\_cqc\_lang}~{X0}})}}}})}}}\label{hyp:ggdgcdpfdgbhdgpfmgbgoghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjdcd}(m1\_subset\_1~X2~X0))\end{array}
\label{hyp:egehpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~(k38\_substut1~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k3\_qc\_lang1~X0)))){\unicdbdjdcd}((\\
v1\_sublemma~(k7\_sublemma~X0~X1~X2)~X0){\unicdcdcdhd}(m1\_subset\_1~(k7\_sublemma~\\
X0~X1~X2)~(k2\_zfmisc\_1~(k16\_substut1~X0)~(k3\_qc\_lang1~X0))))\end{array}
\label{hyp:egehpflghdpfdhfhcgmgfgngngbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}(m1\_subset\_1~(k3\_qc\_lang1~X0)~(k1\_zfmisc\_1~\\
(k2\_qc\_lang1~X0)))\end{array}
\label{hyp:egehpflgddpfbhdgpfmgbgoghgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}(m1\_subset\_1~(k3\_cqc\_lang~X0)~(k1\_zfmisc\_1~\\
(k9\_qc\_lang1~X0)))\end{array}
\label{hyp:egehpflgddpfdgbhdgpfmgbgoghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}(m1\_subset\_1~(k38\_substut1~X0)~(\\
k1\_zfmisc\_1~(k16\_substut1~X0)))\end{array}
\label{hyp:egehpflgddidpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k16\_substut1~\\
X0))){\unicdbdjdcd}(m1\_subset\_1~(k32\_substut1~X0~X1)~(k2\_zfmisc\_1~(k9\_qc\_lang1~\\
X0)~(k1\_substut1~X0)))\end{array}
\label{hyp:egehpflgddcdpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k38\_substut1~\\
X0))){\unicdbdjdcd}(m2\_subset\_1~(k2\_sublemma~X0~X1)~(k9\_qc\_lang1~X0)~(k3\_cqc\_lang~\\
X0))\end{array}
\label{hyp:egehpflgcdpfdhfhcgmgfgngngbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~(k2\_zfmisc\_1~(k16\_substut1~X0)~(k3\_qc\_lang1~X0))){\unicdcdcdhd}(m1\_substut1~\\
X2~X0~X1))){\unicdbdjdcd}(m1\_subset\_1~(k24\_substut1~X0~X1~X2)~(k16\_substut1~\\
X0))\end{array}
\label{hyp:egehpflgcdedpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k16\_substut1~\\
X0))){\unicdbdjdcd}(m1\_subset\_1~(k18\_substut1~X0~X1)~(k9\_qc\_lang1~X0))\end{array}
\label{hyp:egehpflgbdidpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k4\_tarski~X0~X1=k2\_tarski~(k2\_tarski~X0~\\
X1)~(k1\_tarski~X0)\end{array}
\label{hyp:egfdpfehbgchdhlgjg}
\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}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k2\_zfmisc\_1~\\
(k9\_qc\_lang1~X0)~(k1\_substut1~X0))){\unicdbdjdcd}(((k21\_qc\_lang1~X0~(k33\_substut1~\\
X0~X1) \in k10\_xtuple\_0~(k7\_substut1~X0~(k21\_qc\_lang1~X0~(k33\_substut1~\\
X0~X1))~(k33\_substut1~X0~X1)~(k34\_substut1~X0~X1))){\unicdbdjdcd}(k35\_substut1~\\
X0~X1=k2\_qc\_lang3~X0~(k13\_substut1~X0~(k7\_substut1~X0~(k21\_qc\_lang1~\\
X0~(k33\_substut1~X0~X1))~(k33\_substut1~X0~X1)~(k34\_substut1~X0~X1))~\\
(k22\_qc\_lang1~X0~(k33\_substut1~X0~X1))))){\unicdcdcdhd}((\preoh k21\_qc\_lang1~X0~\\
(k33\_substut1~X0~X1) \in k10\_xtuple\_0~(k7\_substut1~X0~(k21\_qc\_lang1~\\
X0~(k33\_substut1~X0~X1))~(k33\_substut1~X0~X1)~(k34\_substut1~X0~X1))){\unicdbdjdcd}\\
(k35\_substut1~X0~X1=k21\_qc\_lang1~X0~(k33\_substut1~X0~X1)))))\end{array}
\label{hyp:egddgdpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k16\_substut1~\\
X0)){\unicdbdjdcd}(k32\_substut1~X0~X1=X1))\end{array}
\label{hyp:egddfdpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_tarski}~{X0}}~{X1}}={{{k2\_tarski}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_xboole\_0~X1))\end{array}
\label{hyp:dgdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddjdpfdhfhcgmgfgngngbg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~X1~(k2\_qc\_lang1~\\
X0)~(k3\_qc\_lang1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~(k16\_substut1~\\
X0)~(k38\_substut1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_substut1~X3~X0~(k7\_sublemma~\\
X0~X2~X1)){\unicdbdjdcd}(\preoh (v3\_substut1~(k7\_sublemma~X0~X2~X1)~X0){\unicdcdcdhd}((\preoh X1 \in k10\_xtuple\_0~\\
(k7\_substut1~X0~X1~(k11\_cqc\_lang~X0~X1~(k2\_sublemma~X0~X2))~X3)){\unicdcdcdhd}\\
(k35\_substut1~X0~(k32\_substut1~X0~(k9\_sublemma~X0~(k7\_sublemma~\\
X0~X2~X1)~X3)) \in k10\_xtuple\_0~(k7\_substut1~X0~X1~(k11\_cqc\_lang~X0~\\
X1~(k2\_sublemma~X0~X2))~X3)))))))\end{array}$$
\end{theorem}
\end{document}
