\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{t45\_lpspace2 (TMXwFguFJQ8LchFtCwZPcC2ECiyzSLhqvUJ)}
\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 $ v10\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_supinf\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_measure1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_lpspace2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k5\_lpspace2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k3\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_mesfunc6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{\preoh{{({{X0} \in {X1}})}}}{\unicdcdcdhd}{({{v1\_xboole\_0}~{X1}})}}}}\label{hyp:ehhdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\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 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~X1~k7\_numbers){\unicdcdcdhd}((v10\_valued\_0~X2){\unicdcdcdhd}((v6\_supinf\_2~X2){\unicdcdcdhd}((v4\_measure1~\\
X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~k7\_numbers)))))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X5 .  (\\
(v1\_funct\_1~X5){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~\\
k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X6 .  ((v1\_funct\_1~X6){\unicdcdcdhd}(m1\_subset\_1~X6~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X7 .  ((v2\_xxreal\_0~\\
X7){\unicdcdcdhd}(m1\_subset\_1~X7~k1\_numbers)){\unicdbdjdcd}(((k5\_lpspace2~X0~X1~X2~X3~X7=\\
k5\_lpspace2~X0~X1~X2~X4~X7){\unicdcdcdhd}(k5\_lpspace2~X0~X1~X2~X5~X7=k5\_lpspace2~\\
X0~X1~X2~X6~X7)){\unicdbdjdcd}(({\unicdcdadad} X8 .  (m2\_subset\_1~X8~(k1\_zfmisc\_1~X0)~X1){\unicdbdjdcd}\\
(\preoh (k1\_funct\_1~X2~(k3\_subset\_1~X0~X8)=k6\_numbers){\unicdcdcdhd}((X8=k1\_relset\_1~\\
X0~X3){\unicdcdcdhd}(r1\_mesfunc6~X0~X1~X3~X8)))){\unicdcdcdid}(({\unicdcdadad} X8 .  (m2\_subset\_1~\\
X8~(k1\_zfmisc\_1~X0)~X1){\unicdbdjdcd}(\preoh (k1\_funct\_1~X2~(k3\_subset\_1~X0~X8)=k6\_numbers){\unicdcdcdhd}\\
((X8=k1\_relset\_1~X0~X4){\unicdcdcdhd}(r1\_mesfunc6~X0~X1~X4~X8)))){\unicdcdcdid}(({\unicdcdadad} X8 .  \\
(m2\_subset\_1~X8~(k1\_zfmisc\_1~X0)~X1){\unicdbdjdcd}(\preoh (k1\_funct\_1~X2~(k3\_subset\_1~\\
X0~X8)=k6\_numbers){\unicdcdcdhd}((X8=k1\_relset\_1~X0~X5){\unicdcdcdhd}(r1\_mesfunc6~X0~X1~\\
X5~X8)))){\unicdcdcdid}(({\unicdcdadad} X8 .  (m2\_subset\_1~X8~(k1\_zfmisc\_1~X0)~X1){\unicdbdjdcd}(\\
\preoh (k1\_funct\_1~X2~(k3\_subset\_1~X0~X8)=k6\_numbers){\unicdcdcdhd}((X8=k1\_relset\_1~\\
X0~X6){\unicdcdcdhd}(r1\_mesfunc6~X0~X1~X6~X8)))){\unicdcdcdid}((v1\_xboole\_0~(k5\_lpspace2~\\
X0~X1~X2~X3~X7)){\unicdcdcdid}((v1\_xboole\_0~(k5\_lpspace2~X0~X1~X2~X5~X7)){\unicdcdcdid}(k5\_lpspace2~\\
X0~X1~X2~(k3\_valued\_1~X0~k1\_numbers~k1\_numbers~X3~X5)~X7=k5\_lpspace2~\\
X0~X1~X2~(k3\_valued\_1~X0~k1\_numbers~k1\_numbers~X4~X6)~X7)))))))))))))))\end{array}
\label{hyp:ehededpfmgahdhahbgdgfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\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 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~X1~k7\_numbers){\unicdcdcdhd}((v10\_valued\_0~X2){\unicdcdcdhd}((v6\_supinf\_2~X2){\unicdcdcdhd}((v4\_measure1~\\
X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~k7\_numbers)))))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v2\_xxreal\_0~X4){\unicdcdcdhd}(m1\_subset\_1~\\
X4~k1\_numbers)){\unicdbdjdcd}((X3 \in k1\_lpspace2~X0~X1~X2~X4){\unicdbdjdcd}(X3 \in k5\_lpspace2~\\
X0~X1~X2~X3~X4))))))\end{array}
\label{hyp:ehddidpfmgahdhahbgdgfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\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 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~X1~k7\_numbers){\unicdcdcdhd}((v10\_valued\_0~X2){\unicdcdcdhd}((v6\_supinf\_2~X2){\unicdcdcdhd}((v4\_measure1~\\
X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~k7\_numbers)))))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v2\_xxreal\_0~X4){\unicdcdcdhd}(m1\_subset\_1~\\
X4~k1\_numbers)){\unicdbdjdcd}(\preoh (X3 \in k1\_lpspace2~X0~X1~X2~X4){\unicdcdcdhd}({\unicdcdadad} X5 .  (m2\_subset\_1~\\
X5~(k1\_zfmisc\_1~X0)~X1){\unicdbdjdcd}(\preoh (k1\_funct\_1~X2~(k3\_subset\_1~X0~X5)=k6\_numbers){\unicdcdcdhd}\\
((k1\_relset\_1~X0~X3=X5){\unicdcdcdhd}(r1\_mesfunc6~X0~X1~X3~X5)))))))))\end{array}
\label{hyp:ehddfdpfmgahdhahbgdgfgcd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
\begin{theorem}\label{thm:ehedfdpfmgahdhahbgdgfgcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
((v1\_prob\_1~X1~X0){\unicdcdcdhd}((v4\_prob\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~X1~k7\_numbers){\unicdcdcdhd}((v10\_valued\_0~X2){\unicdcdcdhd}((v6\_supinf\_2~X2){\unicdcdcdhd}((v4\_measure1~\\
X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~k7\_numbers)))))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X5 .  (\\
(v1\_funct\_1~X5){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~\\
k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X6 .  ((v1\_funct\_1~X6){\unicdcdcdhd}(m1\_subset\_1~X6~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X7 .  ((v2\_xxreal\_0~\\
X7){\unicdcdcdhd}(m1\_subset\_1~X7~k1\_numbers)){\unicdbdjdcd}(((X3 \in k1\_lpspace2~X0~X1~X2~X7){\unicdcdcdhd}\\
((X4 \in k1\_lpspace2~X0~X1~X2~X7){\unicdcdcdhd}((X5 \in k1\_lpspace2~X0~X1~X2~X7){\unicdcdcdhd}((X6 \in \\
k1\_lpspace2~X0~X1~X2~X7){\unicdcdcdhd}((k5\_lpspace2~X0~X1~X2~X3~X7=k5\_lpspace2~\\
X0~X1~X2~X4~X7){\unicdcdcdhd}(k5\_lpspace2~X0~X1~X2~X5~X7=k5\_lpspace2~X0~X1~X2~X6~X7)))))){\unicdbdjdcd}\\
(k5\_lpspace2~X0~X1~X2~(k3\_valued\_1~X0~k1\_numbers~k1\_numbers~X3~X5)~\\
X7=k5\_lpspace2~X0~X1~X2~(k3\_valued\_1~X0~k1\_numbers~k1\_numbers~X4~\\
X6)~X7)))))))))\end{array}$$
\end{theorem}
\end{document}
