\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=}
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\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
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\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{t29\_mesfunc1 (TMUHbDoXVhjjUNJyztPVeZNYpDjwe5jtvN2)}
\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_numbers : {\iota}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_mesfunc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k17\_mesfunc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_measure6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_finsub\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k16\_mesfunc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{\preoh{{({{X0} \in {X1}})}}}{\unicdcdcdhd}{({{v1\_xboole\_0}~{X1}})}}}}\label{hyp:ehhdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v2\_finsub\_1~X1){\unicdcdcdhd}\\
((v1\_prob\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((X2 \in X1){\unicdcdcdhd}(X3 \in X1)){\unicdbdjdcd}(k6\_subset\_1~\\
X2~X3 \in X1))\end{array}
\label{hyp:ehgdpfngfgbgdhfhchfgbd}
\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}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k7\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (\\
m2\_subset\_1~X3~(k1\_zfmisc\_1~X0)~X1){\unicdbdjdcd}((r1\_mesfunc1~X0~X1~X2~X3){\unicdbdjded}\\
({\unicdcdadad} X4 .  (v1\_xreal\_0~X4){\unicdbdjdcd}(k9\_subset\_1~X0~X3~(k16\_mesfunc1~\\
X0~X2~(k1\_measure6~X4)) \in X1))))))\end{array}
\label{hyp:ehcdidpfngfgdhggfhogdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~k7\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~k7\_numbers){\unicdbdjdcd}((r1\_tarski~X2~(k9\_xtuple\_0~X1)){\unicdbdjdcd}(k9\_subset\_1~\\
X0~X2~(k16\_mesfunc1~X0~X1~X3)=k6\_subset\_1~X2~(k9\_subset\_1~X0~X2~(\\
k17\_mesfunc1~X0~X1~X3)))))\end{array}
\label{hyp:ehbdgdpfngfgdhggfhogdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~k7\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~k7\_numbers){\unicdbdjdcd}((r1\_tarski~X2~(k9\_xtuple\_0~X1)){\unicdbdjdcd}(k9\_subset\_1~\\
X0~X2~(k17\_mesfunc1~X0~X1~X3)=k6\_subset\_1~X2~(k9\_subset\_1~X0~X2~(\\
k16\_mesfunc1~X0~X1~X3)))))\end{array}
\label{hyp:ehbdfdpfngfgdhggfhogdgbd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}(m1\_subset\_1~(k1\_measure6~X0)~k7\_numbers)\end{array}
\label{hyp:egehpflgbdpfngfgbgdhfhchfggd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgedpfihchfgbgmgpfad}
\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}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0))){\unicdbdjdcd}(((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_prob\_1~X1~X0){\unicdcdcdhd}(v4\_prob\_1~X1~X0))){\unicdbdjdcd}\\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v2\_finsub\_1~X1){\unicdcdcdhd}((v1\_prob\_1~X1~X0){\unicdcdcdhd}(v4\_prob\_1~\\
X1~X0)))))\end{array}
\label{hyp:dgdgbdpfahchpgcgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdjdpfngfgdhggfhogdgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
((v1\_prob\_1~X1~X0){\unicdcdcdhd}((v4\_prob\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k7\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (\\
m2\_subset\_1~X3~(k1\_zfmisc\_1~X0)~X1){\unicdbdjdcd}((r1\_tarski~X3~(k9\_xtuple\_0~\\
X2)){\unicdbdjdcd}((r1\_mesfunc1~X0~X1~X2~X3){\unicdbdjded}({\unicdcdadad} X4 .  (v1\_xreal\_0~X4){\unicdbdjdcd}(\\
k9\_subset\_1~X0~X3~(k17\_mesfunc1~X0~X2~(k1\_measure6~X4)) \in X1)))))))\end{array}$$
\end{theorem}
\end{document}
