\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{t62\_scmpds\_6 (TMHgKJVQwd9qzqV3B7fzGiMoMBhzTScf6Ja)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_scmpds\_2 : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v5\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_compos\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_scmpds\_4 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_scmpds\_4 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_ami\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_int\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_scmpds\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_scmpds\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k8\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_scmpds\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ r1\_scmpds\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r2\_scmpds\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_scmpds\_4 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~\\
X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_partfun1~\\
X0~k5\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_funct\_1~\\
X1~(k2\_memstr\_0~np\_\_2~k1\_scmpds\_2)){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~\\
k1\_scmpds\_2)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X2~(u1\_compos\_1~\\
k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_finset\_1~X2){\unicdcdcdhd}(v1\_afinsq\_1~\\
X2))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_ami\_2~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(u1\_struct\_0~\\
k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X4 .  (v1\_int\_1~X4){\unicdbdjdcd}((k1\_funct\_1~X1~(k2\_scmpds\_2~\\
(k1\_funct\_1~X1~X3)~X4)=k6\_numbers){\unicdbdjdcd}((r1\_scmpds\_6~(k6\_scmpds\_6~\\
X3~X4~X2)~X1~X0){\unicdcdcdhd}(r2\_scmpds\_6~(k6\_scmpds\_6~X3~X4~X2)~X1~X0)))))))\end{array}
\label{hyp:ehfdjdpfdhdgngahegdhpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~\\
X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_partfun1~\\
X0~k5\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_funct\_1~\\
X1~(k2\_memstr\_0~np\_\_2~k1\_scmpds\_2)){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~\\
k1\_scmpds\_2)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X2~(u1\_compos\_1~\\
k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_finset\_1~X2){\unicdcdcdhd}((v1\_afinsq\_1~\\
X2){\unicdcdcdhd}(v3\_scmpds\_4~X2)))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_ami\_2~X3){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X4 .  (v1\_int\_1~X4){\unicdbdjdcd}((\\
(r1\_scmpds\_6~X2~X1~X0){\unicdcdcdhd}(r2\_scmpds\_6~X2~X1~X0)){\unicdbdjdcd}((k1\_funct\_1~X1~\\
(k2\_scmpds\_2~(k1\_funct\_1~X1~X3)~X4)=k6\_numbers){\unicdcdcdid}((r1\_scmpds\_6~\\
(k6\_scmpds\_6~X3~X4~X2)~X1~X0){\unicdcdcdhd}(r2\_scmpds\_6~(k6\_scmpds\_6~X3~X4~X2)~\\
X1~X0))))))))\end{array}
\label{hyp:ehfdidpfdhdgngahegdhpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((\\
v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X2~(\\
u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_finset\_1~X2){\unicdcdcdhd}\\
(v1\_afinsq\_1~X2))))))){\unicdbdjdcd}(k5\_card\_1~(k6\_scmpds\_6~X0~X1~X2)=k2\_nat\_1~\\
(k5\_card\_1~X2)~np\_\_2)))\end{array}
\label{hyp:ehfdfdpfdhdgngahegdhpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~\\
X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_partfun1~\\
X0~k5\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_funct\_1~\\
X1~(k2\_memstr\_0~np\_\_2~k1\_scmpds\_2)){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~\\
k1\_scmpds\_2)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X2~(u1\_compos\_1~\\
k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_finset\_1~X2){\unicdcdcdhd}((v1\_afinsq\_1~\\
X2){\unicdcdcdhd}(v2\_compos\_1~X2~k1\_scmpds\_2)))))))){\unicdbdjdcd}(((r1\_scmpds\_6~X2~X1~\\
X0){\unicdcdcdhd}(r2\_scmpds\_6~X2~X1~X0)){\unicdbdjdcd}(k5\_memstr\_0~np\_\_2~k1\_scmpds\_2~(k6\_scmpds\_4~\\
X2~(k8\_memstr\_0~np\_\_2~k1\_scmpds\_2~X1)~X0)=k5\_card\_1~X2))))\end{array}
\label{hyp:ehddedpfdhdgngahegdhpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~\\
X0~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}(\\
(v1\_funct\_1~X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_afinsq\_1~X0))))))){\unicdbdjdcd}(\\
(v2\_scmpds\_4~X0){\unicdbdjded}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_funct\_1~\\
X1~(k2\_memstr\_0~np\_\_2~k1\_scmpds\_2)){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~\\
k1\_scmpds\_2)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~\\
X2~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X2~(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}(\\
(v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~k5\_numbers))))){\unicdbdjdcd}(r2\_scmpds\_6~\\
X0~X1~X2))))\end{array}
\label{hyp:ehcdbdpfdhdgngahegdhpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~\\
X0~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}(\\
(v1\_funct\_1~X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_afinsq\_1~X0))))))){\unicdbdjdcd}(\\
(v1\_scmpds\_4~X0){\unicdbdjded}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_funct\_1~\\
X1~(k2\_memstr\_0~np\_\_2~k1\_scmpds\_2)){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~\\
k1\_scmpds\_2)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~\\
X2~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X2~(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}(\\
(v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~k5\_numbers))))){\unicdbdjdcd}(r1\_scmpds\_6~\\
X0~X1~X2))))\end{array}
\label{hyp:ehcdadpfdhdgngahegdhpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_relat\_1~\\
X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X0~(u1\_compos\_1~\\
k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}((v1\_afinsq\_1~\\
X0){\unicdcdcdhd}(v2\_compos\_1~X0~k1\_scmpds\_2)))))))){\unicdcdcdhd}(((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(u1\_struct\_0~k1\_scmpds\_2))){\unicdcdcdhd}(v1\_int\_1~X2))){\unicdbdjdcd}((\preoh v1\_xboole\_0~\\
(k6\_scmpds\_6~X1~X2~X0)){\unicdcdcdhd}((v1\_relat\_1~(k6\_scmpds\_6~X1~X2~X0)){\unicdcdcdhd}(\\
(v4\_relat\_1~(k6\_scmpds\_6~X1~X2~X0)~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~(\\
k6\_scmpds\_6~X1~X2~X0)~(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~\\
(k6\_scmpds\_6~X1~X2~X0)){\unicdcdcdhd}((v1\_finset\_1~(k6\_scmpds\_6~X1~X2~X0)){\unicdcdcdhd}\\
((v1\_afinsq\_1~(k6\_scmpds\_6~X1~X2~X0)){\unicdcdcdhd}(v2\_compos\_1~(k6\_scmpds\_6~\\
X1~X2~X0)~k1\_scmpds\_2))))))))\end{array}
\label{hyp:ggdgbdadpfdhdgngahegdhpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(u1\_struct\_0~k1\_scmpds\_2))){\unicdcdcdhd}((v1\_int\_1~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
X2){\unicdcdcdhd}((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~\\
X2~(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_finset\_1~\\
X2){\unicdcdcdhd}(v1\_afinsq\_1~X2))))))))){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k6\_scmpds\_6~X0~\\
X1~X2)){\unicdcdcdhd}((v1\_relat\_1~(k6\_scmpds\_6~X0~X1~X2)){\unicdcdcdhd}((v4\_relat\_1~(k6\_scmpds\_6~\\
X0~X1~X2)~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~(k6\_scmpds\_6~X0~X1~X2)~(u1\_compos\_1~\\
k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~(k6\_scmpds\_6~X0~X1~X2)){\unicdcdcdhd}((v1\_finset\_1~\\
(k6\_scmpds\_6~X0~X1~X2)){\unicdcdcdhd}(v1\_afinsq\_1~(k6\_scmpds\_6~X0~X1~X2))))))))\end{array}
\label{hyp:egehpflggdpfdhdgngahegdhpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~\\
X0~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}(\\
(v1\_funct\_1~X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}((v1\_afinsq\_1~X0){\unicdcdcdhd}(v2\_scmpds\_4~\\
X0)))))))){\unicdbdjdcd}((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~\\
X0~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}(\\
(v1\_funct\_1~X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}((v1\_afinsq\_1~X0){\unicdcdcdhd}(v1\_scmpds\_4~\\
X0))))))))\end{array}
\label{hyp:dgdgbdpfdhdgngahegdhpfed}
\end{equation}
\begin{theorem}\label{thm:ehgdcdpfdhdgngahegdhpfgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~\\
X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_partfun1~\\
X0~k5\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_funct\_1~\\
X1~(k2\_memstr\_0~np\_\_2~k1\_scmpds\_2)){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~\\
k1\_scmpds\_2)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X2~(u1\_compos\_1~\\
k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_finset\_1~X2){\unicdcdcdhd}((v1\_afinsq\_1~\\
X2){\unicdcdcdhd}((v2\_compos\_1~X2~k1\_scmpds\_2){\unicdcdcdhd}((v2\_scmpds\_4~X2){\unicdcdcdhd}(v3\_scmpds\_4~\\
X2)))))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_ami\_2~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(u1\_struct\_0~\\
k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X4 .  (v1\_int\_1~X4){\unicdbdjdcd}(k5\_memstr\_0~np\_\_2~\\
k1\_scmpds\_2~(k6\_scmpds\_4~(k6\_scmpds\_6~X3~X4~X2)~(k8\_memstr\_0~np\_\_2~\\
k1\_scmpds\_2~X1)~X0)=k2\_nat\_1~(k5\_card\_1~X2)~np\_\_2)))))\end{array}$$
\end{theorem}
\end{document}
