\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{t77\_lpspace2 (TMRaQ8WdniCK7aHccQDYZX9cHSmZMmU4SGJ)}
\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 $ k20\_lpspace1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k12\_lpspace2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ r1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_lpspace1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k10\_lpspace2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k19\_lpspace1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k11\_lpspace2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ g1\_normsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ u2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
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}\\
(r1\_funct\_2~(u1\_struct\_0~(k18\_lpspace1~X0~X1~X2))~k1\_numbers~(\\
u1\_struct\_0~(k10\_lpspace2~X0~X1~X2~np\_\_1))~k1\_numbers~(k19\_lpspace1~\\
X0~X1~X2)~(k11\_lpspace2~X0~X1~X2~np\_\_1))))\end{array}
\label{hyp:ehhdgdpfmgahdhahbgdgfgcd}
\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}\\
(k18\_lpspace1~X0~X1~X2=k10\_lpspace2~X0~X1~X2~np\_\_1)))\end{array}
\label{hyp:ehhdfdpfmgahdhahbgdgfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}(((v1\_funct\_1~X4){\unicdcdcdhd}((\\
v1\_funct\_2~X4~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1))))){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~X2~X3){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X2~X3)))))))){\unicdbdjdcd}((r1\_funct\_2~X0~X1~\\
X2~X3~X4~X5){\unicdbdjded}(X4=X5))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchbdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_numbers}}}}\label{hyp:ggdgbdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((\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)))))){\unicdcdcdhd}((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}\\
((v1\_funct\_1~(k19\_lpspace1~X0~X1~X2)){\unicdcdcdhd}((v1\_funct\_2~(k19\_lpspace1~\\
X0~X1~X2)~(u1\_struct\_0~(k18\_lpspace1~X0~X1~X2))~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
(k19\_lpspace1~X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
(k18\_lpspace1~X0~X1~X2))~k1\_numbers)))))\end{array}
\label{hyp:egehpflgbdjdpfmgahdhahbgdgfgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
(((\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)))))){\unicdcdcdhd}(((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)))))))){\unicdcdcdhd}\\
((v2\_xxreal\_0~X3){\unicdcdcdhd}(m1\_subset\_1~X3~k1\_numbers))))){\unicdbdjdcd}((v1\_funct\_1~\\
(k11\_lpspace2~X0~X1~X2~X3)){\unicdcdcdhd}((v1\_funct\_2~(k11\_lpspace2~X0~X1~X2~\\
X3)~(u1\_struct\_0~(k10\_lpspace2~X0~X1~X2~X3))~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
(k11\_lpspace2~X0~X1~X2~X3)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
(k10\_lpspace2~X0~X1~X2~X3))~k1\_numbers)))))\end{array}
\label{hyp:egehpflgbdbdpfmgahdhahbgdgfgcd}
\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}\\
(k20\_lpspace1~X0~X1~X2=g1\_normsp\_1~(u1\_struct\_0~(k18\_lpspace1~\\
X0~X1~X2))~(u2\_struct\_0~(k18\_lpspace1~X0~X1~X2))~(u1\_algstr\_0~(k18\_lpspace1~\\
X0~X1~X2))~(u1\_rlvect\_1~(k18\_lpspace1~X0~X1~X2))~(k19\_lpspace1~X0~\\
X1~X2))))\end{array}
\label{hyp:egcdadpfmgahdhahbgdgfgbd}
\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 .  ((v2\_xxreal\_0~X3){\unicdcdcdhd}(m1\_subset\_1~X3~k1\_numbers)){\unicdbdjdcd}\\
(k12\_lpspace2~X0~X1~X2~X3=g1\_normsp\_1~(u1\_struct\_0~(k10\_lpspace2~\\
X0~X1~X2~X3))~(u2\_struct\_0~(k10\_lpspace2~X0~X1~X2~X3))~(u1\_algstr\_0~\\
(k10\_lpspace2~X0~X1~X2~X3))~(u1\_rlvect\_1~(k10\_lpspace2~X0~X1~X2~X3))~\\
(k11\_lpspace2~X0~X1~X2~X3)))))\end{array}
\label{hyp:egbdddpfmgahdhahbgdgfgcd}
\end{equation}
\begin{theorem}\label{thm:ehhdhdpfmgahdhahbgdgfgcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
((v1\_prob\_1~X1~X0){\unicdcdcdhd}((v4\_prob\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~X1~k7\_numbers){\unicdcdcdhd}((v10\_valued\_0~X2){\unicdcdcdhd}((v6\_supinf\_2~X2){\unicdcdcdhd}((v4\_measure1~\\
X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~k7\_numbers)))))))){\unicdbdjdcd}\\
(k20\_lpspace1~X0~X1~X2=k12\_lpspace2~X0~X1~X2~np\_\_1)))\end{array}$$
\end{theorem}
\end{document}
