\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{t31\_cqc\_sim1 (TMFD4mcoa6BX75uAx3q4tseKurdh5KCxb3d)}
\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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_finsub\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k9\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}}}$ be given.
Let $ k6\_cqc\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k15\_cqc\_sim1 : {{\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\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ r1\_cqc\_sim1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k13\_cqc\_sim1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_setwiseo : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_cqc\_sim1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_cqc\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k30\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_cqc\_sim1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_cqc\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k28\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k16\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_qc\_lang3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
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}
{{\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 .  (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 .  {\unicdcdadad} X1 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k3\_cqc\_lang~\\
X0))){\unicdbdjdcd}(m1\_subset\_1~(k15\_cqc\_sim1~X0~X1)~(k1\_zfmisc\_1~(k4\_zfmisc\_1~\\
(k3\_cqc\_lang~X0)~(k1\_qc\_lang1~X0)~(k5\_finsub\_1~(k3\_qc\_lang1~X0))~\\
(k9\_funct\_2~(k3\_qc\_lang1~X0)~(k3\_qc\_lang1~X0)))))\end{array}
\label{hyp:egehpflgbdfdpfdgbhdgpfdhjgngbd}
\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 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k4\_zfmisc\_1~(k3\_cqc\_lang~X0)~(k1\_qc\_lang1~X0)~(k5\_finsub\_1~(\\
k3\_qc\_lang1~X0))~(k9\_funct\_2~(k3\_qc\_lang1~X0)~(k3\_qc\_lang1~X0))))){\unicdbdjdcd}\\
((X2=k15\_cqc\_sim1~X0~X1){\unicdbdjded}((r1\_cqc\_sim1~X0~X1~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k4\_zfmisc\_1~(k3\_cqc\_lang~X0)~(k1\_qc\_lang1~\\
X0)~(k5\_finsub\_1~(k3\_qc\_lang1~X0))~(k9\_funct\_2~(k3\_qc\_lang1~X0)~\\
(k3\_qc\_lang1~X0))))){\unicdbdjdcd}((r1\_cqc\_sim1~X0~X1~X3){\unicdbdjdcd}(r1\_tarski~X2~X3)))))))\end{array}
\label{hyp:egbdddpfdgbhdgpfdhjgngbd}
\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 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k4\_zfmisc\_1~(k3\_cqc\_lang~X0)~(k1\_qc\_lang1~X0)~(k5\_finsub\_1~(\\
k3\_qc\_lang1~X0))~(k9\_funct\_2~(k3\_qc\_lang1~X0)~(k3\_qc\_lang1~X0))))){\unicdbdjdcd}\\
((r1\_cqc\_sim1~X0~X1~X2){\unicdbdjded}((k5\_domain\_1~(k3\_cqc\_lang~X0)~(k1\_qc\_lang1~\\
X0)~(k5\_finsub\_1~(k3\_qc\_lang1~X0))~(k1\_funct\_2~(k3\_qc\_lang1~X0)~\\
(k3\_qc\_lang1~X0))~X1~(k13\_cqc\_sim1~X0~X1)~(k1\_setwiseo~(k3\_qc\_lang1~\\
X0))~(k11\_cqc\_sim1~(k3\_qc\_lang1~X0)) \in X2){\unicdcdcdhd}(({\unicdcdadad} X3 .  (m2\_subset\_1~\\
X3~(k9\_qc\_lang1~X0)~(k3\_cqc\_lang~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(k1\_qc\_lang1~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(k5\_finsub\_1~\\
(k3\_qc\_lang1~X0))){\unicdbdjdcd}({\unicdcdadad} X6 .  (m2\_funct\_2~X6~(k3\_qc\_lang1~X0)~\\
(k3\_qc\_lang1~X0)~(k9\_funct\_2~(k3\_qc\_lang1~X0)~(k3\_qc\_lang1~X0))){\unicdbdjdcd}\\
((k5\_domain\_1~(k3\_cqc\_lang~X0)~(k1\_qc\_lang1~X0)~(k5\_finsub\_1~\\
(k3\_qc\_lang1~X0))~(k9\_funct\_2~(k3\_qc\_lang1~X0)~(k3\_qc\_lang1~X0))~\\
(k6\_cqc\_lang~X0~X3)~X4~X5~X6 \in X2){\unicdbdjdcd}(k5\_domain\_1~(k3\_cqc\_lang~X0)~\\
(k1\_qc\_lang1~X0)~(k5\_finsub\_1~(k3\_qc\_lang1~X0))~(k9\_funct\_2~(\\
k3\_qc\_lang1~X0)~(k3\_qc\_lang1~X0))~X3~X4~X5~X6 \in X2)))))){\unicdcdcdhd}(({\unicdcdadad} X3 .  \\
(m2\_subset\_1~X3~(k9\_qc\_lang1~X0)~(k3\_cqc\_lang~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m2\_subset\_1~X4~(k9\_qc\_lang1~X0)~(k3\_cqc\_lang~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~(k1\_qc\_lang1~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~\\
(k5\_finsub\_1~(k3\_qc\_lang1~X0))){\unicdbdjdcd}({\unicdcdadad} X7 .  (m2\_funct\_2~X7~(\\
k3\_qc\_lang1~X0)~(k3\_qc\_lang1~X0)~(k9\_funct\_2~(k3\_qc\_lang1~X0)~\\
(k3\_qc\_lang1~X0))){\unicdbdjdcd}((k5\_domain\_1~(k3\_cqc\_lang~X0)~(k1\_qc\_lang1~\\
X0)~(k5\_finsub\_1~(k3\_qc\_lang1~X0))~(k9\_funct\_2~(k3\_qc\_lang1~X0)~\\
(k3\_qc\_lang1~X0))~(k7\_cqc\_lang~X0~X3~X4)~X5~X6~X7 \in X2){\unicdbdjdcd}((k5\_domain\_1~\\
(k3\_cqc\_lang~X0)~(k1\_qc\_lang1~X0)~(k5\_finsub\_1~(k3\_qc\_lang1~X0))~\\
(k9\_funct\_2~(k3\_qc\_lang1~X0)~(k3\_qc\_lang1~X0))~X3~X5~X6~X7 \in X2){\unicdcdcdhd}\\
(k5\_domain\_1~(k3\_cqc\_lang~X0)~(k1\_qc\_lang1~X0)~(k5\_finsub\_1~(\\
k3\_qc\_lang1~X0))~(k9\_funct\_2~(k3\_qc\_lang1~X0)~(k3\_qc\_lang1~X0))~\\
X4~(k30\_qc\_lang1~X0~X5~(k7\_cqc\_sim1~X0~X3))~X6~X7 \in X2)))))))){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
(m2\_subset\_1~X3~(k9\_qc\_lang1~X0)~(k3\_cqc\_lang~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m2\_subset\_1~X4~(k2\_qc\_lang1~X0)~(k3\_qc\_lang1~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~(k1\_qc\_lang1~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~\\
(k5\_finsub\_1~(k3\_qc\_lang1~X0))){\unicdbdjdcd}({\unicdcdadad} X7 .  (m2\_funct\_2~X7~(\\
k3\_qc\_lang1~X0)~(k3\_qc\_lang1~X0)~(k9\_funct\_2~(k3\_qc\_lang1~X0)~\\
(k3\_qc\_lang1~X0))){\unicdbdjdcd}((k5\_domain\_1~(k3\_cqc\_lang~X0)~(k1\_qc\_lang1~\\
X0)~(k5\_finsub\_1~(k3\_qc\_lang1~X0))~(k9\_funct\_2~(k3\_qc\_lang1~X0)~\\
(k3\_qc\_lang1~X0))~(k11\_cqc\_lang~X0~X4~X3)~X5~X6~X7 \in X2){\unicdbdjdcd}(k6\_xtuple\_0~\\
X3~(k28\_qc\_lang1~X0~X5)~(k2\_xboole\_0~X6~(k6\_domain\_1~(k3\_qc\_lang1~\\
X0)~X4))~(k1\_funct\_4~X7~(k16\_funcop\_1~X4~(k2\_qc\_lang3~X0~X5))) \in \\
X2)))))))))))))\end{array}
\label{hyp:egbdcdpfdgbhdgpfdhjgngbd}
\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:ehddbdpfdgbhdgpfdhjgngbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~X1~(k9\_qc\_lang1~\\
X0)~(k3\_cqc\_lang~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~(k9\_qc\_lang1~\\
X0)~(k3\_cqc\_lang~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_qc\_lang1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k5\_finsub\_1~(k3\_qc\_lang1~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m2\_funct\_2~X5~(k3\_qc\_lang1~X0)~(k3\_qc\_lang1~X0)~(\\
k9\_funct\_2~(k3\_qc\_lang1~X0)~(k3\_qc\_lang1~X0))){\unicdbdjdcd}((k5\_domain\_1~\\
(k3\_cqc\_lang~X0)~(k1\_qc\_lang1~X0)~(k5\_finsub\_1~(k3\_qc\_lang1~X0))~\\
(k9\_funct\_2~(k3\_qc\_lang1~X0)~(k3\_qc\_lang1~X0))~(k6\_cqc\_lang~X0~\\
X2)~X3~X4~X5 \in k15\_cqc\_sim1~X0~X1){\unicdbdjdcd}(k5\_domain\_1~(k3\_cqc\_lang~X0)~\\
(k1\_qc\_lang1~X0)~(k5\_finsub\_1~(k3\_qc\_lang1~X0))~(k9\_funct\_2~(\\
k3\_qc\_lang1~X0)~(k3\_qc\_lang1~X0))~X2~X3~X4~X5 \in k15\_cqc\_sim1~X0~X1)))))))\end{array}$$
\end{theorem}
\end{document}
