\documentclass{article}
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\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}
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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{t27\_measure1 (TMMhpjyXN87cKYohBjAnhoeKE7g72LC6RFP)}
\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 $ k7\_numbers : {\iota}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k12\_supinf\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_supinf\_2 : {\iota}$ be given.
Let $ k1\_supinf\_1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\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~k7\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~k7\_numbers){\unicdbdjdcd}({\unicdcdaddd} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((\\
v1\_funct\_2~X4~X1~k7\_numbers){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X1~k7\_numbers))))){\unicdcdcdhd}({\unicdcdadad} X5 .  (m2\_subset\_1~X5~(k1\_zfmisc\_1~\\
X0)~X1){\unicdbdjdcd}(((X5=k1\_xboole\_0){\unicdbdjdcd}(k12\_supinf\_2~X4~X5=X2)){\unicdcdcdhd}((X5{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}\\
(k12\_supinf\_2~X4~X5=X3)))))))\end{array}
\label{hyp:ehcdgdpfngfgbgdhfhchfgbd}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_supinf\_2}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfdhfhahjgogggpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k1\_supinf\_2}}~{k7\_numbers}}\label{hyp:egehpflgbdpfdhfhahjgogggpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k1\_supinf\_1}}~{k7\_numbers}}\label{hyp:egehpflgbdpfdhfhahjgogggpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdhdpfngfgbgdhfhchfgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_prob\_1~X1~X0){\unicdcdcdhd}\\
((v4\_prob\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0)))))){\unicdbdjdcd}({\unicdcdaddd} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~X1~k7\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~k7\_numbers))))){\unicdcdcdhd}\\
({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(k1\_zfmisc\_1~X0)~X1){\unicdbdjdcd}(((X3=k1\_xboole\_0){\unicdbdjdcd}\\
(k12\_supinf\_2~X2~X3=k1\_supinf\_2)){\unicdcdcdhd}((X3{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}(k12\_supinf\_2~\\
X2~X3=k1\_supinf\_1)))))\end{array}$$
\end{theorem}
\end{document}
