\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}
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\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{t2\_measure8 (TMceW4U3BhmNjQSN2Kk7Ufm4tedvutK9igj)}
\maketitle
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 $ k7\_numbers : {\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 $ v6\_supinf\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_mesfunc9 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k19\_supinf\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_mesfunc9 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v7\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v10\_mesfunc5 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_mesfunc5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_rinfsup2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k18\_supinf\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_mesfunc9 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k8\_supinf\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_supinf\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k7\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k7\_numbers))))){\unicdbdjdcd}\\
((v7\_valued\_0~X0){\unicdbdjdcd}((v10\_mesfunc5~X0){\unicdcdcdhd}(k2\_mesfunc5~X0=k1\_rinfsup2~\\
X0)))\end{array}
\label{hyp:ehddhdpfchjgogggdhfhahcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k7\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k7\_numbers))))){\unicdbdjdcd}\\
(r2\_funct\_2~k5\_numbers~k7\_numbers~(k18\_supinf\_2~X0)~(k2\_mesfunc9~\\
X0))\end{array}
\label{hyp:ehbdpfngfgbgdhfhchfgid}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k7\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k7\_numbers))))){\unicdbdjdcd}\\
((v6\_supinf\_2~X0){\unicdbdjdcd}((v6\_supinf\_2~(k2\_mesfunc9~X0)){\unicdcdcdhd}(v7\_valued\_0~\\
(k2\_mesfunc9~X0))))\end{array}
\label{hyp:ehbdgdpfngfgdhggfhogdgjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((v1\_funct\_1~X2){\unicdcdcdhd}\\
((v1\_funct\_2~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1))))){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~X0~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)))))){\unicdbdjdcd}((r2\_funct\_2~X0~X1~X2~\\
X3){\unicdbdjded}(X2=X3))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{v2\_membered}~{k7\_numbers}}\label{hyp:ggdgcdpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v2\_valued\_0~X0))){\unicdbdjdcd}\\
((v1\_funct\_1~(k2\_mesfunc9~X0)){\unicdcdcdhd}((v1\_funct\_2~(k2\_mesfunc9~X0)~\\
k5\_numbers~k7\_numbers){\unicdcdcdhd}(m1\_subset\_1~(k2\_mesfunc9~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k5\_numbers~k7\_numbers)))))\end{array}
\label{hyp:egehpflgcdpfngfgdhggfhogdgjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k7\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k7\_numbers))))){\unicdbdjdcd}\\
((v1\_funct\_1~(k18\_supinf\_2~X0)){\unicdcdcdhd}((v1\_funct\_2~(k18\_supinf\_2~\\
X0)~k5\_numbers~k7\_numbers){\unicdcdcdhd}(m1\_subset\_1~(k18\_supinf\_2~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k5\_numbers~k7\_numbers)))))\end{array}
\label{hyp:egehpflgbdidpfdhfhahjgogggpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v2\_valued\_0~X0))){\unicdbdjdcd}\\
(k3\_mesfunc9~X0=k2\_mesfunc5~(k2\_mesfunc9~X0))\end{array}
\label{hyp:egddpfngfgdhggfhogdgjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v2\_valued\_0~X0))){\unicdbdjdcd}\\
((v1\_mesfunc9~X0){\unicdbdjded}(v10\_mesfunc5~(k2\_mesfunc9~X0)))\end{array}
\label{hyp:egcdpfngfgdhggfhogdgjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k7\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k7\_numbers))))){\unicdbdjdcd}\\
(k1\_rinfsup2~X0=k8\_supinf\_2~(k17\_supinf\_2~X0))\end{array}
\label{hyp:egbdpfchjgogggdhfhahcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k7\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k7\_numbers))))){\unicdbdjdcd}\\
(k19\_supinf\_2~X0=k8\_supinf\_2~(k17\_supinf\_2~(k18\_supinf\_2~X0)))\end{array}
\label{hyp:egbdhdpfdhfhahjgogggpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v1\_relat\_1~X2)\end{array}
\label{hyp:dgdgbdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v2\_membered~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v2\_valued\_0~X2))\end{array}
\label{hyp:dgdgbdhdpfghbgmgfhfgegpfad}
\end{equation}
\begin{theorem}\label{thm:ehcdpfngfgbgdhfhchfgid}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k7\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k7\_numbers))))){\unicdbdjdcd}\\
((v6\_supinf\_2~X0){\unicdbdjdcd}((v1\_mesfunc9~X0){\unicdcdcdhd}(k19\_supinf\_2~X0=k3\_mesfunc9~\\
X0)))\end{array}$$
\end{theorem}
\end{document}
