\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{t11\_measure5 (TMaMNrHsnuQHdbA5re7gCJLHrfKEnvr6Pcp)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_numbers : {\iota}$ be given.
Let $ v6\_xxreal\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_xxreal\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_measure5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_supinf\_2 : {\iota}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xxreal\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xxreal\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xxreal\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xxreal\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k8\_supinf\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_supinf\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_supinf\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_xxreal\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}(k1\_xxreal\_3~X0~(k2\_xxreal\_3~X0)=\\
k6\_numbers)\end{array}
\label{hyp:ehhdpfihihchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}((\\
\preoh r1\_xxreal\_0~X1~X0){\unicdbdjdcd}(k1\_xxreal\_1~X1~X0=k1\_xboole\_0)))\end{array}
\label{hyp:ehcdjdpfihihchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}((\\
(r1\_xxreal\_0~X0~X1){\unicdcdcdhd}(r1\_xxreal\_0~X1~X0)){\unicdbdjdcd}(X0=X1)))\end{array}
\label{hyp:ehbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xxreal\_0}~{X0}})}{\unicdbdjdcd}{({{{{k1\_xxreal\_1}~{X0}}~{X0}}={{k1\_tarski}~{X0}}})}}}\label{hyp:ehbdhdpfihihchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xxreal\_0}~{X0}})}{\unicdbdjdcd}{({{{k2\_xxreal\_2}~{({{k1\_tarski}~{X0}})}}={X0}})}}}\label{hyp:ehbdddpfihihchfgbgmgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xxreal\_0}~{X0}})}{\unicdbdjdcd}{({{{k1\_xxreal\_2}~{({{k1\_tarski}~{X0}})}}={X0}})}}}\label{hyp:ehbdbdpfihihchfgbgmgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v2\_membered}~{X0}})}{\unicdbdjdcd}{({{{k8\_supinf\_2}~{X0}}={{k1\_xxreal\_2}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfdhfhahjgogggpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v2\_membered}~{X0}})}{\unicdbdjdcd}{({{{k7\_supinf\_2}~{X0}}={{k2\_xxreal\_2}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfdhfhahjgogggpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k7\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k7\_numbers)){\unicdbdjdcd}(k4\_supinf\_2~X0~X1=k3\_xxreal\_3~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfdhfhahjgogggpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_supinf\_2}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfdhfhahjgogggpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v6\_xxreal\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v6\_xxreal\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~k1\_numbers))){\unicdbdjdcd}\\
((r1\_tarski~X0~X1){\unicdbdjdcd}(r1\_xxreal\_0~(k2\_measure5~X0)~(k2\_measure5~\\
X1))))\end{array}
\label{hyp:mgbdidpfngfgbgdhfhchfgfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v6\_xxreal\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers))){\unicdbdjdcd}\\
(r1\_xxreal\_0~k6\_numbers~(k2\_measure5~X0))\end{array}
\label{hyp:mgbdhdpfngfgbgdhfhchfgfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v2\_membered~X0){\unicdbdjdcd}(m1\_subset\_1~(k2\_measure5~X0)~k7\_numbers)\end{array}
\label{hyp:egehpflgcdpfngfgbgdhfhchfgfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v2\_membered~X0){\unicdbdjdcd}(((X0{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}(k2\_measure5~\\
X0=k4\_supinf\_2~(k8\_supinf\_2~X0)~(k7\_supinf\_2~X0))){\unicdcdcdhd}((X0=k1\_xboole\_0){\unicdbdjdcd}\\
(k2\_measure5~X0=k1\_supinf\_2)))\end{array}
\label{hyp:eggdpfngfgbgdhfhchfgfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}(k3\_xxreal\_3~\\
X0~X1=k1\_xxreal\_3~X0~(k2\_xxreal\_3~X1)))\end{array}
\label{hyp:egedpfihihchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers)){\unicdbdjdcd}(v3\_membered~\\
X0)\end{array}
\label{hyp:dgdgidpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v3\_membered}~{X0}})}{\unicdbdjdcd}{({{v2\_membered}~{X0}})}}}\label{hyp:dgdgedpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k7\_numbers}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfihihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdbdpfngfgbgdhfhchfgfd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k7\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k7\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v6\_xxreal\_2~X2){\unicdcdcdhd}(m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~k1\_numbers))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v6\_xxreal\_2~X3){\unicdcdcdhd}(\\
m1\_subset\_1~X3~(k1\_zfmisc\_1~k1\_numbers))){\unicdbdjdcd}(((r1\_tarski~X2~X3){\unicdcdcdhd}\\
((X3=k1\_xxreal\_1~X0~X1){\unicdcdcdhd}(r1\_xxreal\_0~X1~X0))){\unicdbdjdcd}((k2\_measure5~\\
X2=k1\_supinf\_2){\unicdcdcdhd}(k2\_measure5~X3=k1\_supinf\_2))))))\end{array}$$
\end{theorem}
\end{document}
