\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{t38\_ec\_pf\_2 (TMKL15MCti9HeQuNoJrESHt95LQ3iwaEPND)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_int\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_int\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_ec\_pf\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k7\_ec\_pf\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k4\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k8\_group\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k11\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v6\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v33\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_group\_1 : {{\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 $ v4\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v36\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l5\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k1\_xboole\_0}}~{k4\_ordinal1}}\label{hyp:ehbdpfogfhngfgchbgmgdh}
\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 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\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 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(\\
(m1\_subset\_1~X3~X0){\unicdcdcdhd}((m1\_subset\_1~X4~X1){\unicdcdcdhd}(m1\_subset\_1~X5~X2)))))){\unicdbdjdcd}\\
(k4\_domain\_1~X0~X1~X2~X3~X4~X5=k3\_xtuple\_0~X3~X4~X5)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfegpgngbgjgogpfbd}
\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}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~X3~(k3\_zfmisc\_1~\\
X0~X1~X2))))){\unicdbdjdcd}(k3\_mcart\_1~X0~X1~X2~X3=k2\_xtuple\_0~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{k2\_xtuple\_0}~{({{{k4\_tarski}~{X0}}~{X1}})}}={X1}}}}\label{hyp:chegcdpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}((\preoh v6\_struct\_0~\\
(k9\_int\_3~X0)){\unicdcdcdhd}((v13\_algstr\_0~(k9\_int\_3~X0)){\unicdcdcdhd}((v33\_algstr\_0~\\
(k9\_int\_3~X0)){\unicdcdcdhd}((v3\_group\_1~(k9\_int\_3~X0)){\unicdcdcdhd}((v5\_group\_1~(k9\_int\_3~\\
X0)){\unicdcdcdhd}((v2\_rlvect\_1~(k9\_int\_3~X0)){\unicdcdcdhd}((v3\_rlvect\_1~(k9\_int\_3~X0)){\unicdcdcdhd}\\
((v4\_rlvect\_1~(k9\_int\_3~X0)){\unicdcdcdhd}((v4\_vectsp\_1~(k9\_int\_3~X0)){\unicdcdcdhd}(\\
v5\_vectsp\_1~(k9\_int\_3~X0)))))))))))\end{array}
\label{hyp:ggdghdpfjgogehpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v7\_ordinal1~X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k9\_int\_3~X0)){\unicdcdcdhd}(v36\_algstr\_0~(k9\_int\_3~X0)))\end{array}
\label{hyp:ggdggdpfjgogehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdgcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjdcd}(m1\_subset\_1~X2~X0))\end{array}
\label{hyp:egehpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l6\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l2\_algstr\_0}~{X0}})}{\unicdcdcdhd}{({{l5\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmggdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l2\_struct\_0}~{X0}})}{\unicdcdcdhd}{({{l1\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmgcdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{l6\_algstr\_0}~{({{k9\_int\_3}~{X0}})}})}}}\label{hyp:egehpflgjdpfjgogehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k3\_ec\_pf\_1~(k9\_int\_3~X0)))){\unicdbdjdcd}(m2\_subset\_1~(k7\_ec\_pf\_2~X0~X1)~\\
(k3\_zfmisc\_1~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~\\
X0))~(u1\_struct\_0~(k9\_int\_3~X0)))~(k3\_ec\_pf\_1~(k9\_int\_3~X0)))\end{array}
\label{hyp:egehpflghdpffgdgpfahggpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v33\_algstr\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}(\\
(v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~\\
X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdbdjdcd}((\preoh v1\_xboole\_0~\\
(k3\_ec\_pf\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~(k3\_ec\_pf\_1~X0)~(k1\_zfmisc\_1~(\\
k3\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)))))\end{array}
\label{hyp:egehpflgddpffgdgpfahggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~\\
X1~(k3\_zfmisc\_1~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~\\
X0))~(u1\_struct\_0~(k9\_int\_3~X0)))~(k3\_ec\_pf\_1~(k9\_int\_3~X0))){\unicdbdjdcd}\\
(((k3\_mcart\_1~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~\\
X0))~(u1\_struct\_0~(k9\_int\_3~X0))~X1{\unicdcdgdad}k6\_numbers){\unicdbdjdcd}(k7\_ec\_pf\_2~\\
X0~X1=k4\_domain\_1~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~\\
X0))~k5\_numbers~(k8\_group\_1~(k9\_int\_3~X0)~(k1\_mcart\_1~(u1\_struct\_0~\\
(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~\\
X0))~X1)~(k11\_algstr\_0~(k9\_int\_3~X0)~(k3\_mcart\_1~(u1\_struct\_0~\\
(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~\\
X0))~X1)))~(k8\_group\_1~(k9\_int\_3~X0)~(k2\_mcart\_1~(u1\_struct\_0~\\
(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~\\
X0))~X1)~(k11\_algstr\_0~(k9\_int\_3~X0)~(k3\_mcart\_1~(u1\_struct\_0~\\
(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~\\
X0))~X1)))~np\_\_1)){\unicdcdcdhd}((k3\_mcart\_1~(u1\_struct\_0~(k9\_int\_3~X0))~(\\
u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~X0))~X1=k6\_numbers){\unicdbdjdcd}\\
(k7\_ec\_pf\_2~X0~X1=k4\_domain\_1~k5\_numbers~k5\_numbers~k5\_numbers~\\
k6\_numbers~np\_\_1~k6\_numbers))))\end{array}
\label{hyp:eghdpffgdgpfahggpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k3\_xtuple\_0~X0~X1~X2=k4\_tarski~\\
(k4\_tarski~X0~X1)~X2\end{array}
\label{hyp:egedpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)))\end{array}
\label{hyp:dgdgddpfjgogehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_xboole\_0~X1))\end{array}
\label{hyp:dgdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddidpffgdgpfahggpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~(k9\_int\_3~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(\\
u1\_struct\_0~(k9\_int\_3~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(k3\_zfmisc\_1~\\
(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~\\
(k9\_int\_3~X0)))~(k3\_ec\_pf\_1~(k9\_int\_3~X0))){\unicdbdjdcd}((k3\_mcart\_1~(u1\_struct\_0~\\
(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~\\
X0))~(k7\_ec\_pf\_2~X0~X3){\unicdcdgdad}k6\_numbers){\unicdbdjdcd}((k7\_ec\_pf\_2~X0~X3=k4\_domain\_1~\\
(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~X0))~k5\_numbers~\\
(k8\_group\_1~(k9\_int\_3~X0)~(k1\_mcart\_1~(u1\_struct\_0~(k9\_int\_3~\\
X0))~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~X0))~X3)~\\
(k11\_algstr\_0~(k9\_int\_3~X0)~(k3\_mcart\_1~(u1\_struct\_0~(k9\_int\_3~\\
X0))~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~X0))~X3)))~\\
(k8\_group\_1~(k9\_int\_3~X0)~(k2\_mcart\_1~(u1\_struct\_0~(k9\_int\_3~\\
X0))~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~X0))~X3)~\\
(k11\_algstr\_0~(k9\_int\_3~X0)~(k3\_mcart\_1~(u1\_struct\_0~(k9\_int\_3~\\
X0))~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~X0))~X3)))~\\
np\_\_1){\unicdcdcdhd}(k3\_mcart\_1~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~\\
(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~X0))~X3{\unicdcdgdad}k6\_numbers))))))\end{array}$$
\end{theorem}
\end{document}
