\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{t40\_cqc\_sim1 (TMdDrNUm9pns1bRjZT4quHXoWECiEXXPDHF)}
\maketitle
Let $ m1\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_qc\_lang1 : {{\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 $ k3\_cqc\_lang : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k3\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_finsub\_1 : {{\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 $ k15\_cqc\_sim1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_qc\_lang3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_setwiseo : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ r2\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_qc\_lang1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_qc\_lang1~X0)){\unicdbdjdcd}({\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 .  \\
(m2\_funct\_2~X5~(k3\_qc\_lang1~X0)~(k3\_qc\_lang1~X0)~(k9\_funct\_2~(\\
k3\_qc\_lang1~X0)~(k3\_qc\_lang1~X0))){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~\\
X6~(k5\_finsub\_1~(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))~X3~X1~X6~X5 \in k15\_cqc\_sim1~X0~X4){\unicdcdcdhd}\\
(k2\_qc\_lang3~X0~X2 \in k8\_setwiseo~(k3\_qc\_lang1~X0)~(k3\_qc\_lang1~\\
X0)~X5~X6)){\unicdbdjdcd}(r2\_qc\_lang1~X0~X2~X1))))))))\end{array}
\label{hyp:ehddjdpfdgbhdgpfdhjgngbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_qc\_lang1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_qc\_lang1~X0)){\unicdbdjdcd}((r2\_qc\_lang1~\\
X0~X1~X2){\unicdbdjded}((r1\_qc\_lang1~X0~X1~X2){\unicdcdcdhd}(X1{\unicdcdgdad}X2)))))\end{array}
\label{hyp:egddedpfbhdgpfmgbgoghgbd}
\end{equation}
\begin{theorem}\label{thm:ehedadpfdgbhdgpfdhjgngbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_qc\_lang1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~(k9\_qc\_lang1~X0)~(k3\_cqc\_lang~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(k9\_qc\_lang1~X0)~(k3\_cqc\_lang~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_funct\_2~X4~(k3\_qc\_lang1~X0)~(k3\_qc\_lang1~\\
X0)~(k9\_funct\_2~(k3\_qc\_lang1~X0)~(k3\_qc\_lang1~X0))){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~(k5\_finsub\_1~(k3\_qc\_lang1~X0))){\unicdbdjdcd}(\preoh (k5\_domain\_1~\\
(k3\_cqc\_lang~X0)~(k1\_qc\_lang1~X0)~(k5\_finsub\_1~(k3\_qc\_lang1~X0))~\\
(k9\_funct\_2~(k3\_qc\_lang1~X0)~(k3\_qc\_lang1~X0))~X2~X1~X5~X4 \in k15\_cqc\_sim1~\\
X0~X3){\unicdcdcdhd}(k2\_qc\_lang3~X0~X1 \in k8\_setwiseo~(k3\_qc\_lang1~X0)~(k3\_qc\_lang1~\\
X0)~X4~X5)))))))\end{array}$$
\end{theorem}
\end{document}
