\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{t17\_cfcont\_1 (TMZqNk9Y1eczwfBcw5FukfmFpwKK1BAHRsq)}
\maketitle
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k2\_numbers : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m2\_valued\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v2\_comseq\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_comseq\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k8\_comseq\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_comseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_seq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k2\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k2\_numbers))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~k5\_numbers~k2\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k2\_numbers))))){\unicdbdjdcd}\\
((m2\_valued\_0~X0~k2\_numbers~X1){\unicdbdjdcd}((m2\_valued\_0~(k7\_comseq\_3~X0)~\\
k1\_numbers~(k7\_comseq\_3~X1)){\unicdcdcdhd}(m2\_valued\_0~(k8\_comseq\_3~X0)~k1\_numbers~\\
(k8\_comseq\_3~X1)))))\end{array}
\label{hyp:ehedjdpfdgpgngdhfgbhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k2\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k2\_numbers))))){\unicdbdjdcd}\\
(((v2\_comseq\_2~(k7\_comseq\_3~X0)){\unicdcdcdhd}(v2\_comseq\_2~(k8\_comseq\_3~\\
X0))){\unicdbdjdcd}((v2\_comseq\_2~X0){\unicdcdcdhd}((k3\_complex1~(k3\_comseq\_2~X0)=k2\_seq\_2~\\
(k7\_comseq\_3~X0)){\unicdcdcdhd}(k4\_complex1~(k3\_comseq\_2~X0)=k2\_seq\_2~(k8\_comseq\_3~\\
X0)))))\end{array}
\label{hyp:ehedcdpfdgpgngdhfgbhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k2\_numbers){\unicdcdcdhd}\\
((v2\_comseq\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k5\_numbers~k2\_numbers)))))){\unicdbdjdcd}((v2\_comseq\_2~(k7\_comseq\_3~X0)){\unicdcdcdhd}\\
((v2\_comseq\_2~(k8\_comseq\_3~X0)){\unicdcdcdhd}((k2\_seq\_2~(k7\_comseq\_3~X0)=\\
k3\_complex1~(k3\_comseq\_2~X0)){\unicdcdcdhd}(k2\_seq\_2~(k8\_comseq\_3~X0)=k4\_complex1~\\
(k3\_comseq\_2~X0)))))\end{array}
\label{hyp:ehedbdpfdgpgngdhfgbhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}\\
(((m2\_valued\_0~X0~k1\_numbers~X1){\unicdcdcdhd}(v2\_comseq\_2~X1)){\unicdbdjdcd}(v2\_comseq\_2~\\
X0)))\end{array}
\label{hyp:ehbdgdpfdhfgbhpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k2\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k2\_numbers))))){\unicdbdjdcd}\\
((v1\_funct\_1~(k8\_comseq\_3~X0)){\unicdcdcdhd}((v1\_funct\_2~(k8\_comseq\_3~X0)~\\
k5\_numbers~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~(k8\_comseq\_3~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k5\_numbers~k1\_numbers)))))\end{array}
\label{hyp:egehpflgidpfdgpgngdhfgbhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k2\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k2\_numbers))))){\unicdbdjdcd}\\
((v1\_funct\_1~(k7\_comseq\_3~X0)){\unicdcdcdhd}((v1\_funct\_2~(k7\_comseq\_3~X0)~\\
k5\_numbers~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~(k7\_comseq\_3~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k5\_numbers~k1\_numbers)))))\end{array}
\label{hyp:egehpflghdpfdgpgngdhfgbhpfdd}
\end{equation}
\begin{theorem}\label{thm:ehbdhdpfdgggdgpgogehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k2\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k2\_numbers))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~k5\_numbers~k2\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k2\_numbers))))){\unicdbdjdcd}\\
(((m2\_valued\_0~X0~k2\_numbers~X1){\unicdcdcdhd}(v2\_comseq\_2~X1)){\unicdbdjdcd}(v2\_comseq\_2~\\
X0)))\end{array}$$
\end{theorem}
\end{document}
