\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\unicdcdbdgd{\setminus}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t29\_qc\_lang4 (TMWjcDJAZ38nAokU64jzY5Pp6YULc2q2NSx)}
\maketitle
Let $ m1\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_trees\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_qc\_lang4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k3\_qc\_lang4 : {{\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 .  (m1\_subset\_1~X1~(k9\_qc\_lang1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k9\_qc\_lang1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(k9\_qc\_lang1~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_trees\_1~X4~\\
(k9\_xtuple\_0~(k2\_qc\_lang4~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_trees\_1~X5~\\
(k9\_xtuple\_0~(k2\_qc\_lang4~X0~X2))){\unicdbdjdcd}(((X4 \in k3\_qc\_lang4~X0~X1~X2){\unicdcdcdhd}\\
(X5 \in k3\_qc\_lang4~X0~X2~X3)){\unicdbdjdcd}(k8\_finseq\_1~k5\_numbers~X4~X5 \in k3\_qc\_lang4~\\
X0~X1~X3)))))))\end{array}
\label{hyp:ehcdhdpfbhdgpfmgbgoghged}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_tarski~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X0){\unicdbdjdcd}\\
(X2 \in X1))\end{array}
\label{hyp:egddpfehbgchdhlgjg}
\end{equation}
\begin{theorem}\label{thm:ehcdjdpfbhdgpfmgbgoghged}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k9\_qc\_lang1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k9\_qc\_lang1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(k9\_qc\_lang1~X0)){\unicdbdjdcd}(r1\_tarski~(ReplSep2~(toset~\\
({\uniddcgcg} X4 : \iota .  m1\_trees\_1~X4~(k9\_xtuple\_0~(k2\_qc\_lang4~X0~X1))))~\\
({\uniddcgcg} X4 : \iota .  toset~({\uniddcgcg} X5 : \iota .  m1\_trees\_1~X5~(k9\_xtuple\_0~(k2\_qc\_lang4~\\
X0~X2))))~({\uniddcgcg} X4 : \iota .  {\uniddcgcg} X5 : \iota .  (X4 \in k3\_qc\_lang4~X0~X1~X2){\unicdcdcdhd}(\\
X5 \in k3\_qc\_lang4~X0~X2~X3))~({\uniddcgcg} X4 : \iota .  {\uniddcgcg} X5 : \iota .  k8\_finseq\_1~\\
k5\_numbers~X4~X5))~(k3\_qc\_lang4~X0~X1~X3)))))\end{array}$$
\end{theorem}
\end{document}
