\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{t57\_ec\_pf\_1 (TMU6ynZQ6PPACAv6s7M4X9vjDXztmem7Vyq)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_relat\_2 : {{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k8\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_wsierp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_prob\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k16\_rvsum\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_partfun1~X1~X0){\unicdcdcdhd}\\
((v3\_relat\_2~X1){\unicdcdcdhd}((v8\_relat\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v5\_relat\_1~\\
X2~(k8\_eqrel\_1~X0~X1)){\unicdcdcdhd}(v1\_funct\_1~X2))){\unicdbdjdcd}((v2\_funct\_2~X2~(k8\_eqrel\_1~\\
X0~X1)){\unicdbdjdcd}(k3\_card\_3~X2=X0))))\end{array}
\label{hyp:ehfdgdpffgdgpfahggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_partfun1~X1~X0){\unicdcdcdhd}\\
((v3\_relat\_2~X1){\unicdcdcdhd}((v8\_relat\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v5\_relat\_1~\\
X2~(k8\_eqrel\_1~X0~X1)){\unicdcdcdhd}(v1\_funct\_1~X2))){\unicdbdjdcd}((v2\_funct\_1~X2){\unicdbdjdcd}(v1\_prob\_2~\\
X2))))\end{array}
\label{hyp:ehfdfdpffgdgpfahggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_partfun1~X1~X0){\unicdcdcdhd}((v3\_relat\_2~X1){\unicdcdcdhd}((v8\_relat\_2~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v5\_relat\_1~X2~(k8\_eqrel\_1~X0~X1)){\unicdcdcdhd}(v1\_funct\_1~X2))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(X3 \in k9\_xtuple\_0~X2){\unicdbdjdcd}((v1\_finset\_1~(k1\_funct\_1~X2~X3)){\unicdcdcdhd}(m1\_subset\_1~\\
(k1\_funct\_1~X2~X3)~(k1\_zfmisc\_1~X0))))))\end{array}
\label{hyp:ehfdedpffgdgpfahggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_1~\\
X1~k5\_numbers){\unicdbdjdcd}(((v1\_prob\_2~X0){\unicdcdcdhd}((k9\_xtuple\_0~X0=k4\_finseq\_1~\\
X1){\unicdcdcdhd}({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}((X2 \in k9\_xtuple\_0~X0){\unicdbdjdcd}((v1\_finset\_1~\\
(k1\_funct\_1~X0~X2)){\unicdcdcdhd}(k1\_funct\_1~X1~X2=k1\_card\_1~(k1\_funct\_1~X0~\\
X2))))))){\unicdbdjdcd}((v1\_finset\_1~(k3\_card\_3~X0)){\unicdcdcdhd}(k1\_card\_1~(k3\_card\_3~\\
X0)=k16\_rvsum\_1~X1))))\end{array}
\label{hyp:ehbdhdpfegjgdhehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_finset\_1}~{X0}})}{\unicdbdjdcd}{({{{k5\_card\_1}~{X0}}={{k1\_card\_1}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_finseq\_1~X0~k5\_numbers){\unicdbdjdcd}(k2\_wsierp\_1~X0=k16\_rvsum\_1~\\
X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfhhdhjgfgchahpfbd}
\end{equation}
\begin{theorem}\label{thm:ehfdhdpffgdgpfahggpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_partfun1~X1~X0){\unicdcdcdhd}((v3\_relat\_2~X1){\unicdcdcdhd}((v8\_relat\_2~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v5\_relat\_1~X2~(k8\_eqrel\_1~X0~X1)){\unicdcdcdhd}(v1\_funct\_1~X2))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m2\_finseq\_1~X3~k5\_numbers){\unicdbdjdcd}(((v2\_funct\_1~X2){\unicdcdcdhd}((v2\_funct\_2~\\
X2~(k8\_eqrel\_1~X0~X1)){\unicdcdcdhd}((k9\_xtuple\_0~X2=k4\_finseq\_1~X3){\unicdcdcdhd}({\unicdcdadad} X4 .  \\
(v7\_ordinal1~X4){\unicdbdjdcd}((X4 \in k9\_xtuple\_0~X2){\unicdbdjdcd}(k1\_funct\_1~X3~X4=k1\_card\_1~\\
(k1\_funct\_1~X2~X4))))))){\unicdbdjdcd}(k5\_card\_1~X0=k2\_wsierp\_1~X3)))))\end{array}$$
\end{theorem}
\end{document}
