\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{t46\_lpspace2 (TMcNCt2rY4KYxw37kS53pwhGAw46FQC2Ntb)}
\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 $ k5\_lpspace2 : {{\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 $ k26\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ r1\_lpspace1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ v3\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\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 .  (\\
(v2\_xxreal\_0~X5){\unicdcdcdhd}(m1\_subset\_1~X5~k1\_numbers)){\unicdbdjdcd}((r1\_lpspace1~\\
X0~X1~X2~X3~X4){\unicdbdjdcd}(k5\_lpspace2~X0~X1~X2~X3~X5=k5\_lpspace2~X0~X1~X2~X4~X5)))))))\end{array}
\label{hyp:ehedbdpfmgahdhahbgdgfgcd}
\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 .  (\\
(v2\_xxreal\_0~X5){\unicdcdcdhd}(m1\_subset\_1~X5~k1\_numbers)){\unicdbdjdcd}((k5\_lpspace2~\\
X0~X1~X2~X4~X5=k5\_lpspace2~X0~X1~X2~X3~X5){\unicdbdjdcd}(({\unicdcdadad} X6 .  (m2\_subset\_1~\\
X6~(k1\_zfmisc\_1~X0)~X1){\unicdbdjdcd}(\preoh (k1\_funct\_1~X2~(k3\_subset\_1~X0~X6)=k6\_numbers){\unicdcdcdhd}\\
((X6=k1\_relset\_1~X0~X3){\unicdcdcdhd}(r1\_mesfunc6~X0~X1~X3~X6)))){\unicdcdcdid}((k5\_lpspace2~\\
X0~X1~X2~X4~X5=k1\_xboole\_0){\unicdcdcdid}(r1\_lpspace1~X0~X1~X2~X4~X3)))))))))\end{array}
\label{hyp:ehddjdpfmgahdhahbgdgfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~\\
X1){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_prob\_1~X2~X1){\unicdcdcdhd}((v4\_prob\_1~\\
X2~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_zfmisc\_1~X1)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~X2~k7\_numbers){\unicdcdcdhd}((v10\_valued\_0~\\
X3){\unicdcdcdhd}((v6\_supinf\_2~X3){\unicdcdcdhd}((v4\_measure1~X3~X1~X2){\unicdcdcdhd}(m1\_subset\_1~X3~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X2~k7\_numbers)))))))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~\\
k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~X5){\unicdcdcdhd}(m1\_subset\_1~X5~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~k1\_numbers)))){\unicdbdjdcd}((r1\_lpspace1~X1~\\
X2~X3~X4~X5){\unicdbdjdcd}(r1\_lpspace1~X1~X2~X3~(k26\_valued\_1~X1~k1\_numbers~X4~\\
X0)~(k26\_valued\_1~X1~k1\_numbers~X5~X0))))))))\end{array}
\label{hyp:ehddcdpfmgahdhahbgdgfgbd}
\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 .  {\unicdcdaddd} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)){\unicdcdcdhd}(v1\_xboole\_0~\\
X1)\end{array}
\label{hyp:chdgcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v3\_membered}~{k1\_numbers}}\label{hyp:ggdgddpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v3\_membered~X1){\unicdcdcdhd}\\
(((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1)))){\unicdcdcdhd}(v1\_xreal\_0~X3))){\unicdbdjdcd}((v1\_funct\_1~(k26\_valued\_1~X0~X1~\\
X2~X3)){\unicdcdcdhd}(m1\_subset\_1~(k26\_valued\_1~X0~X1~X2~X3)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~k1\_numbers))))\end{array}
\label{hyp:egehpflgcdgdpfghbgmgfhfgegpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehedgdpfmgahdhahbgdgfgcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
((v1\_prob\_1~X1~X0){\unicdcdcdhd}((v4\_prob\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~X1~k7\_numbers){\unicdcdcdhd}((v10\_valued\_0~X2){\unicdcdcdhd}((v6\_supinf\_2~X2){\unicdcdcdhd}((v4\_measure1~\\
X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~k7\_numbers)))))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X5 .  (\\
m1\_subset\_1~X5~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X6 .  ((v2\_xxreal\_0~X6){\unicdcdcdhd}(m1\_subset\_1~\\
X6~k1\_numbers)){\unicdbdjdcd}((k5\_lpspace2~X0~X1~X2~X3~X6=k5\_lpspace2~X0~X1~X2~\\
X4~X6){\unicdbdjdcd}(({\unicdcdadad} X7 .  (m2\_subset\_1~X7~(k1\_zfmisc\_1~X0)~X1){\unicdbdjdcd}(\preoh (k1\_funct\_1~\\
X2~(k3\_subset\_1~X0~X7)=k6\_numbers){\unicdcdcdhd}((k1\_relset\_1~X0~X3=X7){\unicdcdcdhd}(\\
r1\_mesfunc6~X0~X1~X3~X7)))){\unicdcdcdid}(({\unicdcdadad} X7 .  (m2\_subset\_1~X7~(k1\_zfmisc\_1~\\
X0)~X1){\unicdbdjdcd}(\preoh (k1\_funct\_1~X2~(k3\_subset\_1~X0~X7)=k6\_numbers){\unicdcdcdhd}((k1\_relset\_1~\\
X0~X4=X7){\unicdcdcdhd}(r1\_mesfunc6~X0~X1~X4~X7)))){\unicdcdcdid}((v1\_xboole\_0~(k5\_lpspace2~\\
X0~X1~X2~X3~X6)){\unicdcdcdid}(k5\_lpspace2~X0~X1~X2~(k26\_valued\_1~X0~k1\_numbers~\\
X3~X5)~X6=k5\_lpspace2~X0~X1~X2~(k26\_valued\_1~X0~k1\_numbers~X4~X5)~\\
X6)))))))))))\end{array}$$
\end{theorem}
\end{document}
