\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{t25\_measure8 (TMT6bTMJTTDyncesPVRBPQC8kuRebKyLCHS)}
\maketitle
Let $ m1\_measure4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_measure4 : {{\iota}{\unicdbdjdcd}{{\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 $ k9\_setfam\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ k1\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
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.
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 .  ((v5\_relat\_1~X2~X1){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(\\
(v1\_funct\_2~X2~k5\_numbers~(k9\_setfam\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k9\_setfam\_1~X0))))))){\unicdbdjdcd}\\
(k1\_prob\_1~X0~X2 \in X1))\end{array}
\label{hyp:ehbdhdpfahchpgcgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_measure4~X1~X0){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k1\_measure4~\\
X0~X1)){\unicdcdcdhd}((v1\_prob\_1~(k1\_measure4~X0~X1)~X0){\unicdcdcdhd}((v4\_prob\_1~(k1\_measure4~\\
X0~X1)~X0){\unicdcdcdhd}(m1\_subset\_1~(k1\_measure4~X0~X1)~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0))))))\end{array}
\label{hyp:ehbdcdpfngfgbgdhfhchfged}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k9\_setfam\_1}~{X0}}={{k1\_zfmisc\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfdhfgehggbgngpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdfdpfngfgbgdhfhchfgid}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_measure4~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v5\_relat\_1~\\
X2~(k1\_measure4~X0~X1)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~k5\_numbers~\\
(k9\_setfam\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k5\_numbers~(k9\_setfam\_1~X0))))))){\unicdbdjdcd}(k1\_prob\_1~X0~X2 \in k1\_measure4~\\
X0~X1))\end{array}$$
\end{theorem}
\end{document}
