\documentclass{article}
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\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
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\begin{document}
\title{t52\_mesfunc5 (TMNUQ9m6uNDRSsgQHkCFooELE9oUbBntv6X)}
\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 $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k8\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v7\_mesfunc5 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_mesfunc5 : {{\iota}{\unicdbdjdcd}{\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 $ k3\_extreal1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\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 $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_measure6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v10\_mesfunc5 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_supinf\_1 : {\iota}$ be given.
Let $ v8\_mesfunc5 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_supinf\_1 : {\iota}$ be given.
Let $ v9\_mesfunc5 : {{\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 .  (m1\_subset\_1~X0~k7\_numbers){\unicdbdjdcd}((X0=k6\_numbers){\unicdbdjded}(k3\_extreal1~\\
X0=k6\_numbers))\end{array}
\label{hyp:ehfdpffgihehchfgbgmgcd}
\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}
{{\unicdcdaddd} X0 .  {{({\preoh{{{v1\_xboole\_0}~{X0}}}})}{\unicdcdcdhd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:chdgfdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\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}
\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\_mesfunc5~X0){\unicdbdjded}({\unicdcdaddd} X1 .  (v1\_xreal\_0~X1){\unicdcdcdhd}({\unicdcdadad} X2 .  (\\
v1\_xreal\_0~X2){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X2~k6\_numbers){\unicdcdcdhd}({\unicdcdadad} X3 .  (\\
v7\_ordinal1~X3){\unicdbdjdcd}({\unicdcdaddd} X4 .  (v7\_ordinal1~X4){\unicdcdcdhd}((r1\_xxreal\_0~\\
X3~X4){\unicdcdcdhd}(r1\_xxreal\_0~X2~(k3\_extreal1~(k4\_supinf\_2~(k8\_nat\_1~k7\_numbers~\\
X0~X4)~(k1\_measure6~X1)))))))))))\end{array}
\label{hyp:egidpfngfgdhggfhogdgfd}
\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}
{{\unicdcdadad} X0 .  {{({{v1\_xxreal\_0}~{X0}})}{\unicdbdjdcd}{({{{k1\_measure6}~{X0}}={X0}})}}}\label{hyp:egbdpfngfgbgdhfhchfggd}
\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}\\
((v10\_mesfunc5~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k7\_numbers){\unicdbdjdcd}\\
((X1=k2\_mesfunc5~X0){\unicdbdjded}(\preoh ({\unicdcdadad} X2 .  (v1\_xreal\_0~X2){\unicdbdjdcd}(\preoh (X1=X2){\unicdcdcdhd}\\
(({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X3~k6\_numbers){\unicdcdcdhd}\\
({\unicdcdadad} X4 .  (v7\_ordinal1~X4){\unicdbdjdcd}({\unicdcdaddd} X5 .  (v7\_ordinal1~X5){\unicdcdcdhd}(\\
(r1\_xxreal\_0~X4~X5){\unicdcdcdhd}(r1\_xxreal\_0~X3~(k3\_extreal1~(k4\_supinf\_2~\\
(k8\_nat\_1~k7\_numbers~X0~X5)~X1)))))))){\unicdcdcdhd}(v7\_mesfunc5~X0)))){\unicdcdcdhd}(\\
(\preoh (X1=k1\_supinf\_1){\unicdcdcdhd}(v8\_mesfunc5~X0)){\unicdcdcdhd}(\preoh (X1=k2\_supinf\_1){\unicdcdcdhd}\\
(v9\_mesfunc5~X0)))))))\end{array}
\label{hyp:egbdcdpfngfgdhggfhogdgfd}
\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}\\
((v10\_mesfunc5~X0){\unicdbdjded}(\preoh (\preoh v7\_mesfunc5~X0){\unicdcdcdhd}((\preoh v8\_mesfunc5~X0){\unicdcdcdhd}\\
(\preoh v9\_mesfunc5~X0))))\end{array}
\label{hyp:egbdbdpfngfgdhggfhogdgfd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdghdpfpgchegjgogbgmgbd}
\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}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgcdpfihihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehfdcdpfngfgdhggfhogdgfd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k7\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k7\_numbers))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}(({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}(\\
k8\_nat\_1~k7\_numbers~X0~X2=X1)){\unicdbdjdcd}((v7\_mesfunc5~X0){\unicdcdcdhd}(k2\_mesfunc5~\\
X0=X1))))\end{array}$$
\end{theorem}
\end{document}
