\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{t34\_hilbert3 (TMcKWQdRcvKUHhZGxgQSvdBf2MYgpX2QuiS)}
\maketitle
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_hilbert3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_hilbert3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_hilbert2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\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 $ k4\_ordinal1 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k4\_hilbert3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_hilbert1 : {\iota}$ be given.
Let $ k2\_hilbert3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_msualg\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k2\_hilbert1 : {\iota}$ be given.
Let $ k6\_partfun1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_hilbert3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_hilbert1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k16\_funct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k3\_hilbert1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_hilbert3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k5\_numbers}}~{({{k1\_zfmisc\_1}~{k1\_numbers}})}}\label{hyp:egehpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v2\_relat\_1~X0){\unicdcdcdhd}((\\
v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_partfun1~X0~k5\_numbers))))){\unicdcdcdhd}\\
(m1\_hilbert3~X1~X0)){\unicdbdjdcd}(m2\_pboole~(k4\_hilbert3~X0~X1)~k1\_hilbert1~\\
(k2\_hilbert3~X0)~(k2\_hilbert3~X0))\end{array}
\label{hyp:egehpflgedpfigjgmgcgfgchehdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}(m1\_subset\_1~(k1\_hilbert2~\\
X0)~k1\_hilbert1)\end{array}
\label{hyp:egehpflgbdpfigjgmgcgfgchehcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v2\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~\\
k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_partfun1~X0~k5\_numbers))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_hilbert3~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_hilbert1){\unicdbdjdcd}\\
(k5\_hilbert3~X0~X1~X2=k1\_msualg\_3~k1\_hilbert1~(k2\_hilbert3~X0)~\\
(k2\_hilbert3~X0)~(k4\_hilbert3~X0~X1)~X2)))\end{array}
\label{hyp:eggdpfigjgmgcgfgchehdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v2\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~\\
k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_partfun1~X0~k5\_numbers))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_hilbert3~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_pboole~X2~k1\_hilbert1~\\
(k2\_hilbert3~X0)~(k2\_hilbert3~X0)){\unicdbdjdcd}((X2=k4\_hilbert3~X0~X1){\unicdbdjded}(\\
(k1\_msualg\_3~k1\_hilbert1~(k2\_hilbert3~X0)~(k2\_hilbert3~X0)~X2~\\
k2\_hilbert1=k6\_partfun1~np\_\_1){\unicdcdcdhd}(({\unicdcdadad} X3 .  (m2\_subset\_1~X3~\\
k1\_numbers~k5\_numbers){\unicdbdjdcd}(k1\_msualg\_3~k1\_hilbert1~(k2\_hilbert3~\\
X0)~(k2\_hilbert3~X0)~X2~(k1\_hilbert2~X3)=k1\_funct\_1~X1~X3)){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k1\_hilbert1){\unicdbdjdcd}\\
({\unicdcdaddd} X5 .  ((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~(k3\_hilbert3~X0~\\
X3)~(k3\_hilbert3~X0~X3)){\unicdcdcdhd}((v3\_funct\_2~X5~(k3\_hilbert3~X0~X3)~(k3\_hilbert3~\\
X0~X3)){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_hilbert3~\\
X0~X3)~(k3\_hilbert3~X0~X3))))))){\unicdcdcdhd}({\unicdcdaddd} X6 .  ((v1\_funct\_1~X6){\unicdcdcdhd}\\
((v1\_funct\_2~X6~(k3\_hilbert3~X0~X4)~(k3\_hilbert3~X0~X4)){\unicdcdcdhd}((v3\_funct\_2~\\
X6~(k3\_hilbert3~X0~X4)~(k3\_hilbert3~X0~X4)){\unicdcdcdhd}(m1\_subset\_1~X6~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k3\_hilbert3~X0~X4)~(k3\_hilbert3~X0~X4))))))){\unicdcdcdhd}((\\
X5=k1\_msualg\_3~k1\_hilbert1~(k2\_hilbert3~X0)~(k2\_hilbert3~X0)~\\
X2~X3){\unicdcdcdhd}((X6=k1\_msualg\_3~k1\_hilbert1~(k2\_hilbert3~X0)~(k2\_hilbert3~\\
X0)~X2~X4){\unicdcdcdhd}((k1\_msualg\_3~k1\_hilbert1~(k2\_hilbert3~X0)~(k2\_hilbert3~\\
X0)~X2~(k4\_hilbert1~X3~X4)=k16\_funct\_3~(k3\_hilbert3~X0~X3)~(k3\_hilbert3~\\
X0~X4)~(k3\_hilbert3~X0~X3)~(k3\_hilbert3~X0~X4)~X5~X6){\unicdcdcdhd}(k1\_msualg\_3~\\
k1\_hilbert1~(k2\_hilbert3~X0)~(k2\_hilbert3~X0)~X2~(k3\_hilbert1~\\
X3~X4)=k1\_hilbert3~(k3\_hilbert3~X0~X3)~(k3\_hilbert3~X0~X4)~X5~X6)))))))))))))\end{array}
\label{hyp:egfdpfigjgmgcgfgchehdd}
\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:ehddedpfigjgmgcgfgchehdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_relat\_1~X1){\unicdcdcdhd}((v2\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}\\
((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~k5\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_hilbert3~X2~X1){\unicdbdjdcd}(k5\_hilbert3~X1~X2~(k1\_hilbert2~X0)=k1\_funct\_1~\\
X2~X0)))\end{array}$$
\end{theorem}
\end{document}
