\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{t30\_cqc\_the1 (TMSdi3R356WvxWsLJyNpKr9U4JtMLG2VSZR)}
\maketitle
Let $ m1\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_cqc\_lang : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_cqc\_the1 : {\iota}$ be given.
Let $ r2\_cqc\_the1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ np\_\_4 : {\iota}$ be given.
Let $ np\_\_5 : {\iota}$ be given.
Let $ np\_\_6 : {\iota}$ be given.
Let $ np\_\_7 : {\iota}$ be given.
Let $ np\_\_8 : {\iota}$ be given.
Let $ np\_\_9 : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ r1\_cqc\_the1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_cqc\_lang : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ k8\_cqc\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_cqc\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_cqc\_lang : {{\iota}{\unicdbdjdcd}{{\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 $ k24\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k13\_cqc\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{\preoh{{({{X0} \in {X1}})}}}{\unicdcdcdhd}{({{v1\_xboole\_0}~{X1}})}}}}\label{hyp:ehhdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~X1)){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_1~X1~(k2\_zfmisc\_1~\\
(k3\_cqc\_lang~X0)~k2\_cqc\_the1)){\unicdbdjdcd}({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}\\
(\preoh (r1\_xxreal\_0~np\_\_1~X2){\unicdcdcdhd}((r1\_xxreal\_0~X2~(k3\_finseq\_1~X1)){\unicdcdcdhd}\\
((k2\_xtuple\_0~(k1\_funct\_1~X1~X2){\unicdcdgdad}k6\_numbers){\unicdcdcdhd}((k2\_xtuple\_0~\\
(k1\_funct\_1~X1~X2){\unicdcdgdad}np\_\_1){\unicdcdcdhd}((k2\_xtuple\_0~(k1\_funct\_1~X1~X2){\unicdcdgdad}np\_\_2){\unicdcdcdhd}\\
((k2\_xtuple\_0~(k1\_funct\_1~X1~X2){\unicdcdgdad}np\_\_3){\unicdcdcdhd}((k2\_xtuple\_0~(k1\_funct\_1~\\
X1~X2){\unicdcdgdad}np\_\_4){\unicdcdcdhd}((k2\_xtuple\_0~(k1\_funct\_1~X1~X2){\unicdcdgdad}np\_\_5){\unicdcdcdhd}((k2\_xtuple\_0~\\
(k1\_funct\_1~X1~X2){\unicdcdgdad}np\_\_6){\unicdcdcdhd}((k2\_xtuple\_0~(k1\_funct\_1~X1~X2){\unicdcdgdad}np\_\_7){\unicdcdcdhd}\\
((k2\_xtuple\_0~(k1\_funct\_1~X1~X2){\unicdcdgdad}np\_\_8){\unicdcdcdhd}(k2\_xtuple\_0~(k1\_funct\_1~\\
X1~X2){\unicdcdgdad}np\_\_9))))))))))))))\end{array}
\label{hyp:ehcdddpfdgbhdgpfehigfgbd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k3\_cqc\_lang~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~(k2\_zfmisc\_1~\\
(k3\_cqc\_lang~X0)~k2\_cqc\_the1)){\unicdbdjdcd}((r2\_cqc\_the1~X0~X1~X2){\unicdbdjded}((X2{\unicdcdgdad}\\
k1\_xboole\_0){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k5\_numbers){\unicdbdjdcd}(((r1\_xxreal\_0~\\
np\_\_1~X3){\unicdcdcdhd}(r1\_xxreal\_0~X3~(k3\_finseq\_1~X2))){\unicdbdjdcd}(r1\_cqc\_the1~X0~\\
X2~X3~X1)))))))\end{array}
\label{hyp:egfdpfdgbhdgpfehigfgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_1~X1~(k2\_zfmisc\_1~\\
(k3\_cqc\_lang~X0)~k2\_cqc\_the1)){\unicdbdjdcd}({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(k3\_cqc\_lang~X0))){\unicdbdjdcd}\\
(((k2\_xtuple\_0~(k1\_funct\_1~X1~X2)=k6\_numbers){\unicdbdjdcd}((r1\_cqc\_the1~\\
X0~X1~X2~X3){\unicdbdjded}(k1\_xtuple\_0~(k1\_funct\_1~X1~X2) \in X3))){\unicdcdcdhd}(((k2\_xtuple\_0~\\
(k1\_funct\_1~X1~X2)=np\_\_1){\unicdbdjdcd}((r1\_cqc\_the1~X0~X1~X2~X3){\unicdbdjded}(k1\_xtuple\_0~\\
(k1\_funct\_1~X1~X2)=k5\_cqc\_lang~X0))){\unicdcdcdhd}(((k2\_xtuple\_0~(k1\_funct\_1~\\
X1~X2)=np\_\_2){\unicdbdjdcd}((r1\_cqc\_the1~X0~X1~X2~X3){\unicdbdjded}({\unicdcdaddd} X4 .  (m2\_subset\_1~\\
X4~(k9\_qc\_lang1~X0)~(k3\_cqc\_lang~X0)){\unicdcdcdhd}(k1\_xtuple\_0~(k1\_funct\_1~\\
X1~X2)=k8\_cqc\_lang~X0~(k8\_cqc\_lang~X0~(k6\_cqc\_lang~X0~X4)~X4)~X4)))){\unicdcdcdhd}\\
(((k2\_xtuple\_0~(k1\_funct\_1~X1~X2)=np\_\_3){\unicdbdjdcd}((r1\_cqc\_the1~X0~X1~\\
X2~X3){\unicdbdjded}({\unicdcdaddd} X4 .  (m2\_subset\_1~X4~(k9\_qc\_lang1~X0)~(k3\_cqc\_lang~\\
X0)){\unicdcdcdhd}({\unicdcdaddd} X5 .  (m2\_subset\_1~X5~(k9\_qc\_lang1~X0)~(k3\_cqc\_lang~\\
X0)){\unicdcdcdhd}(k1\_xtuple\_0~(k1\_funct\_1~X1~X2)=k8\_cqc\_lang~X0~X4~(k8\_cqc\_lang~\\
X0~(k6\_cqc\_lang~X0~X4)~X5)))))){\unicdcdcdhd}(((k2\_xtuple\_0~(k1\_funct\_1~X1~\\
X2)=np\_\_4){\unicdbdjdcd}((r1\_cqc\_the1~X0~X1~X2~X3){\unicdbdjded}({\unicdcdaddd} X4 .  (m2\_subset\_1~\\
X4~(k9\_qc\_lang1~X0)~(k3\_cqc\_lang~X0)){\unicdcdcdhd}({\unicdcdaddd} X5 .  (m2\_subset\_1~\\
X5~(k9\_qc\_lang1~X0)~(k3\_cqc\_lang~X0)){\unicdcdcdhd}({\unicdcdaddd} X6 .  (m2\_subset\_1~\\
X6~(k9\_qc\_lang1~X0)~(k3\_cqc\_lang~X0)){\unicdcdcdhd}(k1\_xtuple\_0~(k1\_funct\_1~\\
X1~X2)=k8\_cqc\_lang~X0~(k8\_cqc\_lang~X0~X4~X5)~(k8\_cqc\_lang~X0~(k6\_cqc\_lang~\\
X0~(k7\_cqc\_lang~X0~X5~X6))~(k6\_cqc\_lang~X0~(k7\_cqc\_lang~X0~X4~X6))))))))){\unicdcdcdhd}\\
(((k2\_xtuple\_0~(k1\_funct\_1~X1~X2)=np\_\_5){\unicdbdjdcd}((r1\_cqc\_the1~X0~X1~\\
X2~X3){\unicdbdjded}({\unicdcdaddd} X4 .  (m2\_subset\_1~X4~(k9\_qc\_lang1~X0)~(k3\_cqc\_lang~\\
X0)){\unicdcdcdhd}({\unicdcdaddd} X5 .  (m2\_subset\_1~X5~(k9\_qc\_lang1~X0)~(k3\_cqc\_lang~\\
X0)){\unicdcdcdhd}(k1\_xtuple\_0~(k1\_funct\_1~X1~X2)=k8\_cqc\_lang~X0~(k7\_cqc\_lang~\\
X0~X4~X5)~(k7\_cqc\_lang~X0~X5~X4)))))){\unicdcdcdhd}(((k2\_xtuple\_0~(k1\_funct\_1~\\
X1~X2)=np\_\_6){\unicdbdjdcd}((r1\_cqc\_the1~X0~X1~X2~X3){\unicdbdjded}({\unicdcdaddd} X4 .  (m2\_subset\_1~\\
X4~(k9\_qc\_lang1~X0)~(k3\_cqc\_lang~X0)){\unicdcdcdhd}({\unicdcdaddd} X5 .  (m2\_subset\_1~\\
X5~(k2\_qc\_lang1~X0)~(k3\_qc\_lang1~X0)){\unicdcdcdhd}(k1\_xtuple\_0~(k1\_funct\_1~\\
X1~X2)=k8\_cqc\_lang~X0~(k11\_cqc\_lang~X0~X5~X4)~X4))))){\unicdcdcdhd}(((k2\_xtuple\_0~\\
(k1\_funct\_1~X1~X2)=np\_\_7){\unicdbdjdcd}((r1\_cqc\_the1~X0~X1~X2~X3){\unicdbdjded}({\unicdcdaddd} X4 .  \\
(m1\_subset\_1~X4~k5\_numbers){\unicdcdcdhd}({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~k5\_numbers){\unicdcdcdhd}\\
({\unicdcdaddd} X6 .  (m2\_subset\_1~X6~(k9\_qc\_lang1~X0)~(k3\_cqc\_lang~X0)){\unicdcdcdhd}\\
({\unicdcdaddd} X7 .  (m2\_subset\_1~X7~(k9\_qc\_lang1~X0)~(k3\_cqc\_lang~X0)){\unicdcdcdhd}\\
((r1\_xxreal\_0~np\_\_1~X4){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X2~X4){\unicdcdcdhd}((r1\_xxreal\_0~\\
np\_\_1~X5){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X4~X5){\unicdcdcdhd}((X6=k1\_xtuple\_0~(k1\_funct\_1~\\
X1~X5)){\unicdcdcdhd}((X7=k1\_xtuple\_0~(k1\_funct\_1~X1~X2)){\unicdcdcdhd}(k1\_xtuple\_0~(k1\_funct\_1~\\
X1~X4)=k8\_cqc\_lang~X0~X6~X7))))))))))))){\unicdcdcdhd}(((k2\_xtuple\_0~(k1\_funct\_1~\\
X1~X2)=np\_\_8){\unicdbdjdcd}((r1\_cqc\_the1~X0~X1~X2~X3){\unicdbdjded}({\unicdcdaddd} X4 .  (m1\_subset\_1~\\
X4~k5\_numbers){\unicdcdcdhd}({\unicdcdaddd} X5 .  (m2\_subset\_1~X5~(k9\_qc\_lang1~X0)~(\\
k3\_cqc\_lang~X0)){\unicdcdcdhd}({\unicdcdaddd} X6 .  (m2\_subset\_1~X6~(k9\_qc\_lang1~X0)~\\
(k3\_cqc\_lang~X0)){\unicdcdcdhd}({\unicdcdaddd} X7 .  (m2\_subset\_1~X7~(k2\_qc\_lang1~X0)~\\
(k3\_qc\_lang1~X0)){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~X4){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X2~\\
X4){\unicdcdcdhd}((k1\_xtuple\_0~(k1\_funct\_1~X1~X4)=k8\_cqc\_lang~X0~X5~X6){\unicdcdcdhd}((\\
\preoh X7 \in k24\_qc\_lang1~X0~X5){\unicdcdcdhd}(k1\_xtuple\_0~(k1\_funct\_1~X1~X2)=k8\_cqc\_lang~\\
X0~X5~(k11\_cqc\_lang~X0~X7~X6)))))))))))){\unicdcdcdhd}((k2\_xtuple\_0~(k1\_funct\_1~\\
X1~X2)=np\_\_9){\unicdbdjdcd}((r1\_cqc\_the1~X0~X1~X2~X3){\unicdbdjded}({\unicdcdaddd} X4 .  (m1\_subset\_1~\\
X4~k5\_numbers){\unicdcdcdhd}({\unicdcdaddd} X5 .  (m2\_subset\_1~X5~(k2\_qc\_lang1~X0)~(\\
k3\_qc\_lang1~X0)){\unicdcdcdhd}({\unicdcdaddd} X6 .  (m2\_subset\_1~X6~(k2\_qc\_lang1~X0)~\\
(k3\_qc\_lang1~X0)){\unicdcdcdhd}({\unicdcdaddd} X7 .  (m1\_subset\_1~X7~(k9\_qc\_lang1~X0)){\unicdcdcdhd}\\
((r1\_xxreal\_0~np\_\_1~X4){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X2~X4){\unicdcdcdhd}((k13\_cqc\_lang~\\
X0~X7~X5 \in k3\_cqc\_lang~X0){\unicdcdcdhd}((k13\_cqc\_lang~X0~X7~X6 \in k3\_cqc\_lang~X0){\unicdcdcdhd}\\
((\preoh X5 \in k24\_qc\_lang1~X0~X7){\unicdcdcdhd}((k13\_cqc\_lang~X0~X7~X5=k1\_xtuple\_0~\\
(k1\_funct\_1~X1~X4)){\unicdcdcdhd}(k13\_cqc\_lang~X0~X7~X6=k1\_xtuple\_0~(k1\_funct\_1~\\
X1~X2))))))))))))))))))))))))))\end{array}
\label{hyp:egedpfdgbhdgpfehigfgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\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:ehddadpfdgbhdgpfehigfgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k3\_cqc\_lang~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k3\_cqc\_lang~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_finseq\_1~X3~(k2\_zfmisc\_1~\\
(k3\_cqc\_lang~X0)~k2\_cqc\_the1)){\unicdbdjdcd}(((r2\_cqc\_the1~X0~X1~X3){\unicdcdcdhd}(r1\_tarski~\\
X1~X2)){\unicdbdjdcd}(r2\_cqc\_the1~X0~X2~X3)))))\end{array}$$
\end{theorem}
\end{document}
