\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{t18\_mesfun9c (TMYoaWh9Q2EASqm6jwKPg1tv5yPRf9J57Fr)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ 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 $ k4\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_mesfunc5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v1\_mesfunc8 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_mesfunc6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k2\_mesfun9c : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_series\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k10\_seqfunc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r1\_mesfunc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k8\_mesfun7c : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v2\_comseq\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_series\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_rfunct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \preoh (X0 \in X1){\unicdcdcdhd}((m1\_subset\_1~X1~(\\
k1\_zfmisc\_1~X2)){\unicdcdcdhd}(v1\_xboole\_0~X2))\end{array}
\label{hyp:ehfdpfdhfhcgdhfgeh}
\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 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
((v1\_prob\_1~X1~X0){\unicdcdcdhd}((v4\_prob\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)){\unicdcdcdhd}((v1\_mesfunc8~X2~X0~\\
k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
(k4\_partfun1~X0~k1\_numbers))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_subset\_1~\\
X3~(k1\_zfmisc\_1~X0)~X1){\unicdbdjdcd}(((k1\_relset\_1~X0~(k4\_mesfunc5~X0~k1\_numbers~\\
X2~k6\_numbers)=X3){\unicdcdcdhd}(({\unicdcdadad} X4 .  (v7\_ordinal1~X4){\unicdbdjdcd}(r1\_mesfunc6~\\
X0~X1~(k4\_mesfunc5~X0~k1\_numbers~X2~X4)~X3)){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~X0){\unicdbdjdcd}((X4 \in X3){\unicdbdjdcd}(v2\_comseq\_2~(k10\_seqfunc~X0~X2~X4)))))){\unicdbdjdcd}(r1\_mesfunc1~\\
X0~X1~(k8\_mesfun7c~X0~X2)~X3)))))\end{array}
\label{hyp:ehcdbdpfngfgdhggfhoghddg}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k1\_xboole\_0}}~{k4\_ordinal1}}\label{hyp:ehbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)))))){\unicdbdjdcd}\\
((v1\_mesfunc8~X1~X0~k1\_numbers){\unicdbdjdcd}(v1\_mesfunc8~(k2\_mesfun9c~X0~\\
X1)~X0~k1\_numbers)))\end{array}
\label{hyp:ehbdhdpfngfgdhggfhogjddg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_mesfunc8~X1~\\
X0~k1\_numbers){\unicdcdcdhd}((r1\_tarski~X3~(k1\_relset\_1~X0~(k4\_mesfunc5~X0~\\
k1\_numbers~X1~k6\_numbers))){\unicdcdcdhd}(X2 \in X3))){\unicdbdjdcd}((v2\_comseq\_2~(k3\_series\_1~\\
(k10\_seqfunc~X0~X1~X2))){\unicdbdjded}(v2\_comseq\_2~(k10\_seqfunc~X0~(k2\_mesfun9c~\\
X0~X1)~X2))))))\end{array}
\label{hyp:ehbdddpfngfgdhggfhogjddg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}((v1\_mesfunc8~X1~X0~k1\_numbers){\unicdbdjdcd}\\
(k1\_relset\_1~X0~(k4\_mesfunc5~X0~k1\_numbers~(k2\_mesfun9c~X0~X1)~\\
X2)=k1\_relset\_1~X0~(k4\_mesfunc5~X0~k1\_numbers~X1~k6\_numbers)))))\end{array}
\label{hyp:ehbdbdpfngfgdhggfhogjddg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r1\_tarski}~{X0}}~{X0}}}}\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfehbgchdhlgjg}
\end{equation}
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}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k3\_rfunct\_3}~{X0}}~{X1}}={{{k4\_partfun1}~{X0}}~{X1}}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfchggfhogdgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers))))))){\unicdbdjdcd}\\
((v1\_funct\_1~(k2\_mesfun9c~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k2\_mesfun9c~\\
X0~X1)~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)){\unicdcdcdhd}(m1\_subset\_1~(\\
k2\_mesfun9c~X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~\\
X0~k1\_numbers))))))\end{array}
\label{hyp:egehpflgcdpfngfgdhggfhogjddg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v1\_funct\_2~X1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~\\
X0~k1\_numbers)))))){\unicdcdcdhd}(m1\_subset\_1~X2~X0))){\unicdbdjdcd}((v1\_funct\_1~(k10\_seqfunc~\\
X0~X1~X2)){\unicdcdcdhd}((v1\_funct\_2~(k10\_seqfunc~X0~X1~X2)~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~(k10\_seqfunc~X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k5\_numbers~k1\_numbers)))))\end{array}
\label{hyp:egehpflgbdadpfdhfgbhggfhogdg}
\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}\\
((v1\_series\_1~X0){\unicdbdjded}(v2\_comseq\_2~(k3\_series\_1~X0)))\end{array}
\label{hyp:egcdpfdhfgchjgfgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehbdidpfngfgdhggfhogjddg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
((v1\_prob\_1~X1~X0){\unicdcdcdhd}((v4\_prob\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~\\
X0~k1\_numbers)))))){\unicdbdjdcd}(((k1\_relset\_1~X0~(k4\_mesfunc5~X0~k1\_numbers~\\
X3~k6\_numbers)=X2){\unicdcdcdhd}((v1\_mesfunc8~X3~X0~k1\_numbers){\unicdcdcdhd}(({\unicdcdadad} X4 .  \\
(v7\_ordinal1~X4){\unicdbdjdcd}(r1\_mesfunc6~X0~X1~(k4\_mesfunc5~X0~k1\_numbers~\\
(k2\_mesfun9c~X0~X3)~X4)~X2)){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~X0){\unicdbdjdcd}(\\
(X4 \in X2){\unicdbdjdcd}(v1\_series\_1~(k10\_seqfunc~X0~X3~X4))))))){\unicdbdjdcd}(r1\_mesfunc1~\\
X0~X1~(k8\_mesfun7c~X0~(k2\_mesfun9c~X0~X3))~X2)))))\end{array}$$
\end{theorem}
\end{document}
