\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t47\_sublemma (TMPPEey8CVXYscZVPdt7jp8YHAGkTp7bWyS)}
\maketitle
Let $ m1\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k9\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_cqc\_lang : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k24\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_cqc\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_cqc\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_cqc\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k6\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_card\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_cqc\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k12\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k5\_cqc\_lang : {{\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~(k9\_qc\_lang1~\\
X0)~(k3\_cqc\_lang~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~(k2\_qc\_lang1~\\
X0)~(k3\_qc\_lang1~X0)){\unicdbdjdcd}((r1\_tarski~(k24\_qc\_lang1~X0~X1)~(k9\_substut1~\\
X0~X1)){\unicdbdjdcd}(r1\_tarski~(k24\_qc\_lang1~X0~(k11\_cqc\_lang~X0~X2~X1))~(k9\_substut1~\\
X0~(k11\_cqc\_lang~X0~X2~X1))))))\end{array}
\label{hyp:ehedgdpfdhfhcgmgfgngngbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~X1~(k9\_qc\_lang1~\\
X0)~(k3\_cqc\_lang~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~(k9\_qc\_lang1~\\
X0)~(k3\_cqc\_lang~X0)){\unicdbdjdcd}(((r1\_tarski~(k24\_qc\_lang1~X0~X1)~(k9\_substut1~\\
X0~X1)){\unicdcdcdhd}(r1\_tarski~(k24\_qc\_lang1~X0~X2)~(k9\_substut1~X0~X2))){\unicdbdjdcd}\\
(r1\_tarski~(k24\_qc\_lang1~X0~(k7\_cqc\_lang~X0~X1~X2))~(k9\_substut1~\\
X0~(k7\_cqc\_lang~X0~X1~X2))))))\end{array}
\label{hyp:ehedfdpfdhfhcgmgfgngngbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~X1~(k9\_qc\_lang1~\\
X0)~(k3\_cqc\_lang~X0)){\unicdbdjdcd}((r1\_tarski~(k24\_qc\_lang1~X0~X1)~(k9\_substut1~\\
X0~X1)){\unicdbdjdcd}(r1\_tarski~(k24\_qc\_lang1~X0~(k6\_cqc\_lang~X0~X1))~(k9\_substut1~\\
X0~(k6\_cqc\_lang~X0~X1)))))\end{array}
\label{hyp:ehededpfdhfhcgmgfgngngbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k5\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m2\_subset\_1~X2~(k6\_qc\_lang1~X0)~(k8\_qc\_lang1~X0~X1)){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v5\_relat\_1~X3~(k3\_qc\_lang1~X0)){\unicdcdcdhd}((v3\_card\_1~X3~\\
X1){\unicdcdcdhd}(m2\_finseq\_1~X3~(k2\_qc\_lang1~X0)))){\unicdbdjdcd}(k24\_qc\_lang1~X0~(k4\_cqc\_lang~\\
X1~X0~X2~X3)=k9\_substut1~X0~(k4\_cqc\_lang~X1~X0~X2~X3)))))\end{array}
\label{hyp:ehedddpfdhfhcgmgfgngngbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}(k24\_qc\_lang1~X0~(k12\_qc\_lang1~X0)=\\
k1\_xboole\_0)\end{array}
\label{hyp:ehddpfbhdgpfmgbgoghgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}(k9\_substut1~X0~(k5\_cqc\_lang~X0)=\\
k1\_xboole\_0)\end{array}
\label{hyp:ehcdpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}o .  {\unicdcdadad} X1 .  ({\unicdcdadad} X2 .  (m2\_subset\_1~X2~(\\
k9\_qc\_lang1~X1)~(k3\_cqc\_lang~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_subset\_1~X3~\\
(k9\_qc\_lang1~X1)~(k3\_cqc\_lang~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_subset\_1~\\
X4~(k2\_qc\_lang1~X1)~(k3\_qc\_lang1~X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X6 .  ((v5\_relat\_1~X6~(k3\_qc\_lang1~X1)){\unicdcdcdhd}\\
((v3\_card\_1~X6~X5){\unicdcdcdhd}(m2\_finseq\_1~X6~(k2\_qc\_lang1~X1)))){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m2\_subset\_1~X7~(k6\_qc\_lang1~X1)~(k8\_qc\_lang1~X1~X5)){\unicdbdjdcd}((X0~(k5\_cqc\_lang~\\
X1)){\unicdcdcdhd}((X0~(k4\_cqc\_lang~X5~X1~X7~X6)){\unicdcdcdhd}(((X0~X2){\unicdbdjdcd}(X0~(k6\_cqc\_lang~\\
X1~X2))){\unicdcdcdhd}((((X0~X2){\unicdcdcdhd}(X0~X3)){\unicdbdjdcd}(X0~(k7\_cqc\_lang~X1~X2~X3))){\unicdcdcdhd}((X0~\\
X2){\unicdbdjdcd}(X0~(k11\_cqc\_lang~X1~X4~X2))))))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~(k9\_qc\_lang1~X1)~(k3\_cqc\_lang~X1)){\unicdbdjdcd}(X0~X2))\end{array}
\label{hyp:dhbdpfdgbhdgpfmgbgoghg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r1\_tarski}~{X0}}~{X0}}}}\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{m1\_qc\_lang1}~{X0}})}{\unicdbdjdcd}{({{{k5\_cqc\_lang}~{X0}}={{k12\_qc\_lang1}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfdgbhdgpfmgbgoghg}
\end{equation}
\begin{theorem}\label{thm:ehedhdpfdhfhcgmgfgngngbg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~X1~(k9\_qc\_lang1~\\
X0)~(k3\_cqc\_lang~X0)){\unicdbdjdcd}(r1\_tarski~(k24\_qc\_lang1~X0~X1)~(k9\_substut1~\\
X0~X1)))\end{array}$$
\end{theorem}
\end{document}
