\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{l32\_nat\_4 (TMPtVDbKmUV9W7gk3xQ8znjV4L3UgAtGaAK)}
\maketitle
Let $ v1\_int\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ np\_\_6 : {\iota}$ be given.
Let $ np\_\_8 : {\iota}$ be given.
Let $ np\_\_9 : {\iota}$ be given.
Let $ np\_\_10 : {\iota}$ be given.
Let $ np\_\_12 : {\iota}$ be given.
Let $ np\_\_14 : {\iota}$ be given.
Let $ np\_\_15 : {\iota}$ be given.
Let $ np\_\_16 : {\iota}$ be given.
Let $ np\_\_18 : {\iota}$ be given.
Let $ np\_\_20 : {\iota}$ be given.
Let $ np\_\_21 : {\iota}$ be given.
Let $ np\_\_22 : {\iota}$ be given.
Let $ np\_\_24 : {\iota}$ be given.
Let $ np\_\_25 : {\iota}$ be given.
Let $ np\_\_26 : {\iota}$ be given.
Let $ np\_\_27 : {\iota}$ be given.
Let $ np\_\_28 : {\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 $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_7 : {\iota}$ be given.
Let $ np\_\_5 : {\iota}$ be given.
Let $ np\_\_4 : {\iota}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ np\_\_13 : {\iota}$ be given.
Let $ np\_\_11 : {\iota}$ be given.
Let $ k3\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_nat\_d : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_int\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_9){\unicdcdcdhd}(m2\_subset\_1~np\_\_9~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_9~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_9~k1\_numbers))\end{array}
\label{hyp:dhahdgjdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_8){\unicdcdcdhd}(m2\_subset\_1~np\_\_8~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_8~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_8~k1\_numbers))\end{array}
\label{hyp:dhahdgidpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_7){\unicdcdcdhd}(m2\_subset\_1~np\_\_7~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_7~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_7~k1\_numbers))\end{array}
\label{hyp:dhahdghdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_6){\unicdcdcdhd}(m2\_subset\_1~np\_\_6~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_6~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_6~k1\_numbers))\end{array}
\label{hyp:dhahdggdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_5){\unicdcdcdhd}(m2\_subset\_1~np\_\_5~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_5~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_5~k1\_numbers))\end{array}
\label{hyp:dhahdgfdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_4){\unicdcdcdhd}(m2\_subset\_1~np\_\_4~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_4~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_4~k1\_numbers))\end{array}
\label{hyp:dhahdgedpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_3){\unicdcdcdhd}(m2\_subset\_1~np\_\_3~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_3~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_3~k1\_numbers))\end{array}
\label{hyp:dhahdgddpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_2){\unicdcdcdhd}(m2\_subset\_1~np\_\_2~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_2~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_2~k1\_numbers))\end{array}
\label{hyp:dhahdgcdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_28){\unicdcdcdhd}(m2\_subset\_1~np\_\_28~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_28~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_28~k1\_numbers))\end{array}
\label{hyp:dhahdgcdidpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_27){\unicdcdcdhd}(m2\_subset\_1~np\_\_27~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_27~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_27~k1\_numbers))\end{array}
\label{hyp:dhahdgcdhdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_26){\unicdcdcdhd}(m2\_subset\_1~np\_\_26~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_26~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_26~k1\_numbers))\end{array}
\label{hyp:dhahdgcdgdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_25){\unicdcdcdhd}(m2\_subset\_1~np\_\_25~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_25~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_25~k1\_numbers))\end{array}
\label{hyp:dhahdgcdfdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_24){\unicdcdcdhd}(m2\_subset\_1~np\_\_24~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_24~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_24~k1\_numbers))\end{array}
\label{hyp:dhahdgcdedpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_22){\unicdcdcdhd}(m2\_subset\_1~np\_\_22~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_22~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_22~k1\_numbers))\end{array}
\label{hyp:dhahdgcdcdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_21){\unicdcdcdhd}(m2\_subset\_1~np\_\_21~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_21~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_21~k1\_numbers))\end{array}
\label{hyp:dhahdgcdbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_20){\unicdcdcdhd}(m2\_subset\_1~np\_\_20~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_20~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_20~k1\_numbers))\end{array}
\label{hyp:dhahdgcdadpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_18){\unicdcdcdhd}(m2\_subset\_1~np\_\_18~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_18~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_18~k1\_numbers))\end{array}
\label{hyp:dhahdgbdidpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_16){\unicdcdcdhd}(m2\_subset\_1~np\_\_16~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_16~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_16~k1\_numbers))\end{array}
\label{hyp:dhahdgbdgdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_15){\unicdcdcdhd}(m2\_subset\_1~np\_\_15~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_15~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_15~k1\_numbers))\end{array}
\label{hyp:dhahdgbdfdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_14){\unicdcdcdhd}(m2\_subset\_1~np\_\_14~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_14~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_14~k1\_numbers))\end{array}
\label{hyp:dhahdgbdedpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_13){\unicdcdcdhd}(m2\_subset\_1~np\_\_13~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_13~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_13~k1\_numbers))\end{array}
\label{hyp:dhahdgbdddpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_12){\unicdcdcdhd}(m2\_subset\_1~np\_\_12~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_12~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_12~k1\_numbers))\end{array}
\label{hyp:dhahdgbdcdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_11){\unicdcdcdhd}(m2\_subset\_1~np\_\_11~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_11~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_11~k1\_numbers))\end{array}
\label{hyp:dhahdgbdbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_10){\unicdcdcdhd}(m2\_subset\_1~np\_\_10~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_10~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_10~k1\_numbers))\end{array}
\label{hyp:dhahdgbdadpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{{{{k3\_xcmplx\_0}~{np\_\_9}}~{np\_\_3}}={np\_\_27}}\label{hyp:chbhcffgbgmgnefhmgehpfpflgddpfihdgngahmgihpfadpfpfchjdpfchddpfchcdhd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k3\_xcmplx\_0}~{np\_\_6}}~{np\_\_4}}={np\_\_24}}\label{hyp:chbhcffgbgmgnefhmgehpfpflgddpfihdgngahmgihpfadpfpfchgdpfchedpfchcded}
\end{equation}
Assume the following.
\begin{equation}
{{{{k3\_xcmplx\_0}~{np\_\_6}}~{np\_\_3}}={np\_\_18}}\label{hyp:chbhcffgbgmgnefhmgehpfpflgddpfihdgngahmgihpfadpfpfchgdpfchddpfchbdid}
\end{equation}
Assume the following.
\begin{equation}
{{{{k3\_xcmplx\_0}~{np\_\_5}}~{np\_\_5}}={np\_\_25}}\label{hyp:chbhcffgbgmgnefhmgehpfpflgddpfihdgngahmgihpfadpfpfchfdpfchfdpfchcdfd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k3\_xcmplx\_0}~{np\_\_4}}~{np\_\_7}}={np\_\_28}}\label{hyp:chbhcffgbgmgnefhmgehpfpflgddpfihdgngahmgihpfadpfpfchedpfchhdpfchcdid}
\end{equation}
Assume the following.
\begin{equation}
{{{{k3\_xcmplx\_0}~{np\_\_4}}~{np\_\_5}}={np\_\_20}}\label{hyp:chbhcffgbgmgnefhmgehpfpflgddpfihdgngahmgihpfadpfpfchedpfchfdpfchcdad}
\end{equation}
Assume the following.
\begin{equation}
{{{{k3\_xcmplx\_0}~{np\_\_4}}~{np\_\_4}}={np\_\_16}}\label{hyp:chbhcffgbgmgnefhmgehpfpflgddpfihdgngahmgihpfadpfpfchedpfchedpfchbdgd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k3\_xcmplx\_0}~{np\_\_3}}~{np\_\_7}}={np\_\_21}}\label{hyp:chbhcffgbgmgnefhmgehpfpflgddpfihdgngahmgihpfadpfpfchddpfchhdpfchcdbd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k3\_xcmplx\_0}~{np\_\_3}}~{np\_\_5}}={np\_\_15}}\label{hyp:chbhcffgbgmgnefhmgehpfpflgddpfihdgngahmgihpfadpfpfchddpfchfdpfchbdfd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k3\_xcmplx\_0}~{np\_\_3}}~{np\_\_4}}={np\_\_12}}\label{hyp:chbhcffgbgmgnefhmgehpfpflgddpfihdgngahmgihpfadpfpfchddpfchedpfchbdcd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k3\_xcmplx\_0}~{np\_\_3}}~{np\_\_3}}={np\_\_9}}\label{hyp:chbhcffgbgmgnefhmgehpfpflgddpfihdgngahmgihpfadpfpfchddpfchddpfchjd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k3\_xcmplx\_0}~{np\_\_2}}~{np\_\_7}}={np\_\_14}}\label{hyp:chbhcffgbgmgnefhmgehpfpflgddpfihdgngahmgihpfadpfpfchcdpfchhdpfchbded}
\end{equation}
Assume the following.
\begin{equation}
{{{{k3\_xcmplx\_0}~{np\_\_2}}~{np\_\_5}}={np\_\_10}}\label{hyp:chbhcffgbgmgnefhmgehpfpflgddpfihdgngahmgihpfadpfpfchcdpfchfdpfchbdad}
\end{equation}
Assume the following.
\begin{equation}
{{{{k3\_xcmplx\_0}~{np\_\_2}}~{np\_\_4}}={np\_\_8}}\label{hyp:chbhcffgbgmgnefhmgehpfpflgddpfihdgngahmgihpfadpfpfchcdpfchedpfchid}
\end{equation}
Assume the following.
\begin{equation}
{{{{k3\_xcmplx\_0}~{np\_\_2}}~{np\_\_3}}={np\_\_6}}\label{hyp:chbhcffgbgmgnefhmgehpfpflgddpfihdgngahmgihpfadpfpfchcdpfchddpfchgd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k3\_xcmplx\_0}~{np\_\_13}}~{np\_\_2}}={np\_\_26}}\label{hyp:chbhcffgbgmgnefhmgehpfpflgddpfihdgngahmgihpfadpfpfchbdddpfchcdpfchcdgd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k3\_xcmplx\_0}~{np\_\_11}}~{np\_\_2}}={np\_\_22}}\label{hyp:chbhcffgbgmgnefhmgehpfpflgddpfihdgngahmgihpfadpfpfchbdbdpfchcdpfchcdcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}(\\
(r1\_nat\_d~X0~X1){\unicdbdjded}(r1\_int\_1~X0~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchbdpfogbgehpfeg}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((v1\_int\_2~X0){\unicdbdjded}((\preoh r1\_xxreal\_0~X0~\\
np\_\_1){\unicdcdcdhd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}(\preoh (r1\_int\_1~X1~X0){\unicdcdcdhd}((X1{\unicdcdgdad}\\
np\_\_1){\unicdcdcdhd}(X1{\unicdcdgdad}X0))))))\end{array}
\label{hyp:egedpfjgogehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((\\
r1\_nat\_d~X0~X1){\unicdbdjded}({\unicdcdaddd} X2 .  (v7\_ordinal1~X2){\unicdcdcdhd}(X1=k3\_xcmplx\_0~\\
X0~X2))))\end{array}
\label{hyp:egddpfogbgehpfeg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:mgddcdpfogbgehpfed}
$$\begin{array}{c}(\preoh v1\_int\_2~np\_\_6){\unicdcdcdhd}((\preoh v1\_int\_2~np\_\_8){\unicdcdcdhd}((\preoh v1\_int\_2~np\_\_9){\unicdcdcdhd}((\\
\preoh v1\_int\_2~np\_\_10){\unicdcdcdhd}((\preoh v1\_int\_2~np\_\_12){\unicdcdcdhd}((\preoh v1\_int\_2~np\_\_14){\unicdcdcdhd}\\
((\preoh v1\_int\_2~np\_\_15){\unicdcdcdhd}((\preoh v1\_int\_2~np\_\_16){\unicdcdcdhd}((\preoh v1\_int\_2~np\_\_18){\unicdcdcdhd}\\
((\preoh v1\_int\_2~np\_\_20){\unicdcdcdhd}((\preoh v1\_int\_2~np\_\_21){\unicdcdcdhd}((\preoh v1\_int\_2~np\_\_22){\unicdcdcdhd}\\
((\preoh v1\_int\_2~np\_\_24){\unicdcdcdhd}((\preoh v1\_int\_2~np\_\_25){\unicdcdcdhd}((\preoh v1\_int\_2~np\_\_26){\unicdcdcdhd}\\
((\preoh v1\_int\_2~np\_\_27){\unicdcdcdhd}(\preoh v1\_int\_2~np\_\_28))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
