\documentclass{article}
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\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t15\_lp\_space (TMTUnXaAmR6gMetSc7k5mapfiXaPFsFv8ew)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_normsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ g1\_normsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k2\_lp\_space : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_rsspace : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_rsspace : {\iota}$ be given.
Let $ k8\_rsspace : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_rsspace : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_lp\_space : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_normsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}((r1\_xxreal\_0~np\_\_1~X0){\unicdbdjdcd}\\
((\preoh v2\_struct\_0~(g1\_normsp\_1~(k2\_lp\_space~X0)~(k10\_rsspace~k7\_rsspace~\\
(k2\_lp\_space~X0))~(k8\_rsspace~k7\_rsspace~(k2\_lp\_space~X0))~(k9\_rsspace~\\
k7\_rsspace~(k2\_lp\_space~X0))~(k3\_lp\_space~X0))){\unicdcdcdhd}((v13\_algstr\_0~\\
(g1\_normsp\_1~(k2\_lp\_space~X0)~(k10\_rsspace~k7\_rsspace~(k2\_lp\_space~\\
X0))~(k8\_rsspace~k7\_rsspace~(k2\_lp\_space~X0))~(k9\_rsspace~k7\_rsspace~\\
(k2\_lp\_space~X0))~(k3\_lp\_space~X0))){\unicdcdcdhd}((v2\_rlvect\_1~(g1\_normsp\_1~\\
(k2\_lp\_space~X0)~(k10\_rsspace~k7\_rsspace~(k2\_lp\_space~X0))~(k8\_rsspace~\\
k7\_rsspace~(k2\_lp\_space~X0))~(k9\_rsspace~k7\_rsspace~(k2\_lp\_space~\\
X0))~(k3\_lp\_space~X0))){\unicdcdcdhd}((v3\_rlvect\_1~(g1\_normsp\_1~(k2\_lp\_space~\\
X0)~(k10\_rsspace~k7\_rsspace~(k2\_lp\_space~X0))~(k8\_rsspace~k7\_rsspace~\\
(k2\_lp\_space~X0))~(k9\_rsspace~k7\_rsspace~(k2\_lp\_space~X0))~(k3\_lp\_space~\\
X0))){\unicdcdcdhd}((v4\_rlvect\_1~(g1\_normsp\_1~(k2\_lp\_space~X0)~(k10\_rsspace~\\
k7\_rsspace~(k2\_lp\_space~X0))~(k8\_rsspace~k7\_rsspace~(k2\_lp\_space~\\
X0))~(k9\_rsspace~k7\_rsspace~(k2\_lp\_space~X0))~(k3\_lp\_space~X0))){\unicdcdcdhd}\\
((v5\_rlvect\_1~(g1\_normsp\_1~(k2\_lp\_space~X0)~(k10\_rsspace~k7\_rsspace~\\
(k2\_lp\_space~X0))~(k8\_rsspace~k7\_rsspace~(k2\_lp\_space~X0))~(k9\_rsspace~\\
k7\_rsspace~(k2\_lp\_space~X0))~(k3\_lp\_space~X0))){\unicdcdcdhd}((v6\_rlvect\_1~\\
(g1\_normsp\_1~(k2\_lp\_space~X0)~(k10\_rsspace~k7\_rsspace~(k2\_lp\_space~\\
X0))~(k8\_rsspace~k7\_rsspace~(k2\_lp\_space~X0))~(k9\_rsspace~k7\_rsspace~\\
(k2\_lp\_space~X0))~(k3\_lp\_space~X0))){\unicdcdcdhd}((v7\_rlvect\_1~(g1\_normsp\_1~\\
(k2\_lp\_space~X0)~(k10\_rsspace~k7\_rsspace~(k2\_lp\_space~X0))~(k8\_rsspace~\\
k7\_rsspace~(k2\_lp\_space~X0))~(k9\_rsspace~k7\_rsspace~(k2\_lp\_space~\\
X0))~(k3\_lp\_space~X0))){\unicdcdcdhd}((v8\_rlvect\_1~(g1\_normsp\_1~(k2\_lp\_space~\\
X0)~(k10\_rsspace~k7\_rsspace~(k2\_lp\_space~X0))~(k8\_rsspace~k7\_rsspace~\\
(k2\_lp\_space~X0))~(k9\_rsspace~k7\_rsspace~(k2\_lp\_space~X0))~(k3\_lp\_space~\\
X0))){\unicdcdcdhd}(l1\_rlvect\_1~(g1\_normsp\_1~(k2\_lp\_space~X0)~(k10\_rsspace~\\
k7\_rsspace~(k2\_lp\_space~X0))~(k8\_rsspace~k7\_rsspace~(k2\_lp\_space~\\
X0))~(k9\_rsspace~k7\_rsspace~(k2\_lp\_space~X0))~(k3\_lp\_space~X0)))))))))))))\end{array}
\label{hyp:ehidpfmgahpfdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}((r1\_xxreal\_0~np\_\_1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_normsp\_1~X1)){\unicdbdjdcd}((X1=g1\_normsp\_1~\\
(k2\_lp\_space~X0)~(k10\_rsspace~k7\_rsspace~(k2\_lp\_space~X0))~(k8\_rsspace~\\
k7\_rsspace~(k2\_lp\_space~X0))~(k9\_rsspace~k7\_rsspace~(k2\_lp\_space~\\
X0))~(k3\_lp\_space~X0)){\unicdbdjdcd}((v4\_normsp\_0~X1){\unicdcdcdhd}((v3\_normsp\_0~X1){\unicdcdcdhd}\\
(v2\_normsp\_1~X1))))))\end{array}
\label{hyp:ehbdedpfmgahpfdhahbgdgfg}
\end{equation}
\begin{theorem}\label{thm:ehbdfdpfmgahpfdhahbgdgfg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}((r1\_xxreal\_0~np\_\_1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_normsp\_1~X1)){\unicdbdjdcd}((X1=g1\_normsp\_1~\\
(k2\_lp\_space~X0)~(k10\_rsspace~k7\_rsspace~(k2\_lp\_space~X0))~(k8\_rsspace~\\
k7\_rsspace~(k2\_lp\_space~X0))~(k9\_rsspace~k7\_rsspace~(k2\_lp\_space~\\
X0))~(k3\_lp\_space~X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}\\
((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}((v5\_rlvect\_1~\\
X1){\unicdcdcdhd}((v6\_rlvect\_1~X1){\unicdcdcdhd}((v7\_rlvect\_1~X1){\unicdcdcdhd}((v8\_rlvect\_1~X1){\unicdcdcdhd}\\
((v3\_normsp\_0~X1){\unicdcdcdhd}((v4\_normsp\_0~X1){\unicdcdcdhd}((v2\_normsp\_1~X1){\unicdcdcdhd}(l1\_normsp\_1~\\
X1))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
