\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{t11\_scmisort (TMWVv44F5QNofULZKLyp7ZzCFjWCYctmZyB)}
\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\_scmfsa\_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\_\_3 : {\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 $ v1\_ami\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_scmfsa\_m : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_scm\_halt : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r2\_scm\_halt : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k5\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k1\_funct\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_scmfsa\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_scmfsa\_m : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ r5\_scmfsa7b : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r6\_scmfsa7b : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k8\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k18\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v5\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~(u1\_struct\_0~k1\_scmfsa\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X0){\unicdcdcdhd}(v5\_funct\_1~X0~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2))))){\unicdbdjdcd}\\
(k1\_funct\_1~(k1\_scmfsa\_m~X0)~(k4\_scmfsa\_2~k6\_numbers)=np\_\_1)\end{array}
\label{hyp:ehjdpfdhdgngggdhbgpfng}
\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\_scmfsa\_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\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_funct\_1~\\
X1~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2)){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~\\
k1\_scmfsa\_2)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~\\
X2~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X2~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}(\\
(\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_finset\_1~X2){\unicdcdcdhd}(v1\_afinsq\_1~\\
X2))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_ami\_2~X3){\unicdcdcdhd}((\preoh v1\_scmfsa\_m~X3){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(u1\_struct\_0~k1\_scmfsa\_2)))){\unicdbdjdcd}(((r5\_scmfsa7b~X2~X1~X0){\unicdcdcdhd}(r6\_scmfsa7b~\\
X2~X1~X0)){\unicdbdjdcd}((r1\_xxreal\_0~(k1\_funct\_1~X1~X3)~k6\_numbers){\unicdcdcdid}((k5\_memstr\_0~\\
np\_\_3~k1\_scmfsa\_2~(k5\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~\\
X0~(k2\_scmfsa\_9~X3~X2))~(k8\_memstr\_0~np\_\_3~k1\_scmfsa\_2~X1)~(k2\_nat\_1~\\
(k8\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~X0~X2)~(k8\_memstr\_0~\\
np\_\_3~k1\_scmfsa\_2~X1))~np\_\_3))=k6\_numbers){\unicdcdcdhd}({\unicdcdadad} X4 .  (m2\_subset\_1~\\
X4~k1\_numbers~k5\_numbers){\unicdbdjdcd}((r1\_xxreal\_0~X4~(k2\_nat\_1~(k8\_extpro\_1~\\
np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~X0~X2)~(k8\_memstr\_0~np\_\_3~k1\_scmfsa\_2~\\
X1))~np\_\_3)){\unicdbdjdcd}(k5\_memstr\_0~np\_\_3~k1\_scmfsa\_2~(k5\_extpro\_1~np\_\_3~\\
k1\_scmfsa\_2~(k1\_funct\_4~X0~(k2\_scmfsa\_9~X3~X2))~(k8\_memstr\_0~np\_\_3~\\
k1\_scmfsa\_2~X1)~X4) \in k2\_afinsq\_1~(k2\_scmfsa\_9~X3~X2))))))))))\end{array}
\label{hyp:ehedcdpfdhdgngggdhbgpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~(u1\_struct\_0~k1\_scmfsa\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X0){\unicdcdcdhd}((v5\_funct\_1~X0~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X0~(u1\_struct\_0~k1\_scmfsa\_2)))))){\unicdbdjdcd}(({\unicdcdadad} X1 .  \\
((v1\_ami\_2~X1){\unicdcdcdhd}((\preoh v1\_scmfsa\_m~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~\\
k1\_scmfsa\_2)))){\unicdbdjdcd}(k1\_funct\_1~(k1\_scmfsa\_m~X0)~X1=k1\_funct\_1~\\
X0~X1)){\unicdcdcdhd}({\unicdcdadad} X1 .  (m1\_scmfsa\_2~X1){\unicdbdjdcd}(k18\_scmfsa\_2~(k1\_scmfsa\_m~\\
X0)~X1=k18\_scmfsa\_2~X0~X1)))\end{array}
\label{hyp:ehddhdpfdhdgngggdhbgpfng}
\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\_scmfsa\_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\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_funct\_1~\\
X1~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2)){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~\\
k1\_scmfsa\_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\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_finset\_1~X2){\unicdcdcdhd}(v1\_afinsq\_1~\\
X2))))))){\unicdbdjdcd}((r2\_scm\_halt~X2~X1~X0){\unicdbdjded}(r6\_scmfsa7b~X2~(k1\_scmfsa\_m~\\
X1)~X0))))\end{array}
\label{hyp:ehddbdpfdhdgngpfigbgmgeh}
\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\_scmfsa\_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\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_funct\_1~\\
X1~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2)){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~\\
k1\_scmfsa\_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\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_finset\_1~X2){\unicdcdcdhd}(v1\_afinsq\_1~\\
X2))))))){\unicdbdjdcd}((r1\_scm\_halt~X2~X1~X0){\unicdbdjded}(r5\_scmfsa7b~X2~(k1\_scmfsa\_m~\\
X1)~X0))))\end{array}
\label{hyp:ehddadpfdhdgngpfigbgmgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~(u1\_struct\_0~k1\_scmfsa\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X0){\unicdcdcdhd}((v5\_funct\_1~X0~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X0~(u1\_struct\_0~k1\_scmfsa\_2)))))){\unicdbdjdcd}((k1\_funct\_1~\\
X0~(k4\_scmfsa\_2~k6\_numbers)=np\_\_1){\unicdbdjdcd}(k8\_memstr\_0~np\_\_3~k1\_scmfsa\_2~\\
X0=k1\_scmfsa\_m~X0))\end{array}
\label{hyp:ehbdidpfdhdgngggdhbgpfng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v5\_ordinal1~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}(v1\_finset\_1~X0)))){\unicdbdjdcd}(k2\_afinsq\_1~X0=k9\_xtuple\_0~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~(u1\_struct\_0~k1\_scmfsa\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X0){\unicdcdcdhd}(v5\_funct\_1~X0~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2))))){\unicdbdjdcd}\\
(k1\_scmfsa\_m~(k1\_scmfsa\_m~X0)=k1\_scmfsa\_m~X0)\end{array}
\label{hyp:ahchpgkgfgdgehjgghjgehjhpflgbdpfdhdgngggdhbgpfng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~(u1\_struct\_0~k1\_scmfsa\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X0){\unicdcdcdhd}((v5\_funct\_1~X0~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X0~(u1\_struct\_0~k1\_scmfsa\_2)))))){\unicdbdjdcd}((v1\_relat\_1~\\
(k1\_scmfsa\_m~X0)){\unicdcdcdhd}((v4\_relat\_1~(k1\_scmfsa\_m~X0)~(u1\_struct\_0~\\
k1\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~(k1\_scmfsa\_m~X0)){\unicdcdcdhd}((v5\_funct\_1~\\
(k1\_scmfsa\_m~X0)~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2)){\unicdcdcdhd}(v1\_partfun1~\\
(k1\_scmfsa\_m~X0)~(u1\_struct\_0~k1\_scmfsa\_2))))))\end{array}
\label{hyp:ggdgedpfdhdgngggdhbgpfng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(u1\_struct\_0~\\
k1\_scmfsa\_2))){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}\\
((v5\_relat\_1~X1~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_finset\_1~X1){\unicdcdcdhd}(v1\_afinsq\_1~X1)))))))){\unicdbdjdcd}\\
((v1\_relat\_1~(k2\_scmfsa\_9~X0~X1)){\unicdcdcdhd}((v4\_relat\_1~(k2\_scmfsa\_9~\\
X0~X1)~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~(k2\_scmfsa\_9~X0~X1)~(u1\_compos\_1~\\
k1\_scmfsa\_2)){\unicdcdcdhd}((\preoh v1\_xboole\_0~(k2\_scmfsa\_9~X0~X1)){\unicdcdcdhd}((v1\_funct\_1~\\
(k2\_scmfsa\_9~X0~X1)){\unicdcdcdhd}((v1\_finset\_1~(k2\_scmfsa\_9~X0~X1)){\unicdcdcdhd}(v1\_afinsq\_1~\\
(k2\_scmfsa\_9~X0~X1))))))))\end{array}
\label{hyp:egehpflgcdpfdhdgngggdhbgpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~(u1\_struct\_0~k1\_scmfsa\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X0){\unicdcdcdhd}(v5\_funct\_1~X0~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2))))){\unicdbdjdcd}\\
((v1\_relat\_1~(k1\_scmfsa\_m~X0)){\unicdcdcdhd}((v4\_relat\_1~(k1\_scmfsa\_m~X0)~\\
(u1\_struct\_0~k1\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~(k1\_scmfsa\_m~X0)){\unicdcdcdhd}\\
(v5\_funct\_1~(k1\_scmfsa\_m~X0)~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2)))))\end{array}
\label{hyp:egehpflgbdpfdhdgngggdhbgpfng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_afinsq\_1~X0))))){\unicdbdjdcd}((v1\_relat\_1~X0){\unicdcdcdhd}\\
((v5\_ordinal1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)))\end{array}
\label{hyp:dgdgjdpfbgggjgogdhbhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdbdpfdhdgngjgdhpgcheh}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~\\
X0~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_partfun1~\\
X0~k5\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~(u1\_struct\_0~k1\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_funct\_1~\\
X1~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2)){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~\\
k1\_scmfsa\_2)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X2~(u1\_compos\_1~\\
k1\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_finset\_1~X2){\unicdcdcdhd}(v1\_afinsq\_1~\\
X2))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_ami\_2~X3){\unicdcdcdhd}((\preoh v1\_scmfsa\_m~X3){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(u1\_struct\_0~k1\_scmfsa\_2)))){\unicdbdjdcd}(((r1\_scm\_halt~X2~X1~X0){\unicdcdcdhd}(r2\_scm\_halt~\\
X2~X1~X0)){\unicdbdjdcd}((r1\_xxreal\_0~(k1\_funct\_1~X1~X3)~k6\_numbers){\unicdcdcdid}((k5\_memstr\_0~\\
np\_\_3~k1\_scmfsa\_2~(k5\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~\\
X0~(k2\_scmfsa\_9~X3~X2))~(k1\_scmfsa\_m~X1)~(k2\_nat\_1~(k8\_extpro\_1~\\
np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~X0~X2)~(k1\_scmfsa\_m~X1))~np\_\_3))=\\
k6\_numbers){\unicdcdcdhd}({\unicdcdadad} X4 .  (m2\_subset\_1~X4~k1\_numbers~k5\_numbers){\unicdbdjdcd}\\
((r1\_xxreal\_0~X4~(k2\_nat\_1~(k8\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~\\
X0~X2)~(k1\_scmfsa\_m~X1))~np\_\_3)){\unicdbdjdcd}(k5\_memstr\_0~np\_\_3~k1\_scmfsa\_2~\\
(k5\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~X0~(k2\_scmfsa\_9~X3~\\
X2))~(k1\_scmfsa\_m~X1)~X4) \in k9\_xtuple\_0~(k2\_scmfsa\_9~X3~X2))))))))))\end{array}$$
\end{theorem}
\end{document}
