\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{l48\_scmfsa8a (TMRVRZ89yGaP6rVyDdJubHNmS8dEHg1MF2M)}
\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 $ 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 $ 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 $ r5\_scmfsa7b : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_scmfsa\_m : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r6\_scmfsa7b : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ 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 $ k3\_scmfsa6a : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_scmfsa8a : {{\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 $ np\_\_1 : {\iota}$ be given.
Let $ k4\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k16\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k8\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k6\_memstr\_0 : {{\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 $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 .  ((\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\_scmfsa\_2)){\unicdcdcdhd}(\\
(v1\_funct\_1~X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_afinsq\_1~X0))))))){\unicdbdjdcd}(\\
{\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X1~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}((v1\_finset\_1~X1){\unicdcdcdhd}(v1\_afinsq\_1~X1))))))){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~(u1\_struct\_0~k1\_scmfsa\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X2){\unicdcdcdhd}((v5\_funct\_1~X2~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X2~(u1\_struct\_0~k1\_scmfsa\_2)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_relat\_1~X3){\unicdcdcdhd}((v4\_relat\_1~X3~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X3~\\
(u1\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}(v1\_partfun1~X3~\\
k5\_numbers))))){\unicdbdjdcd}(((r5\_scmfsa7b~X0~X2~X3){\unicdcdcdhd}(r6\_scmfsa7b~X0~X2~X3)){\unicdbdjdcd}\\
(r1\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~X3~(k3\_scmfsa6a~(k3\_scmfsa6a~\\
(k3\_scmfsa6a~X0~(k1\_scmfsa8a~(k2\_nat\_1~(k5\_card\_1~X1)~np\_\_1)))~\\
X1)~(k4\_compos\_1~k1\_scmfsa\_2)))~(k8\_memstr\_0~np\_\_3~k1\_scmfsa\_2~\\
X2))))))\end{array}
\label{hyp:ehddidpfdhdgngggdhbgidbg}
\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}((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~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 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_relat\_1~\\
X1){\unicdcdcdhd}((v4\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X1~(u1\_compos\_1~\\
k1\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_finset\_1~X1){\unicdcdcdhd}(v1\_afinsq\_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\_scmfsa\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_finset\_1~X2){\unicdcdcdhd}(v1\_afinsq\_1~X2))))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((v4\_relat\_1~X3~(u1\_struct\_0~k1\_scmfsa\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X3){\unicdcdcdhd}((v5\_funct\_1~X3~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X3~(u1\_struct\_0~k1\_scmfsa\_2)))))){\unicdbdjdcd}(((r5\_scmfsa7b~\\
X1~X3~X0){\unicdcdcdhd}(r6\_scmfsa7b~X1~X3~X0)){\unicdbdjdcd}((k5\_memstr\_0~np\_\_3~k1\_scmfsa\_2~\\
(k5\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~X0~(k3\_scmfsa6a~(k3\_scmfsa6a~\\
(k3\_scmfsa6a~X1~(k1\_scmfsa8a~(k2\_nat\_1~(k5\_card\_1~X2)~np\_\_1)))~\\
X2)~(k4\_compos\_1~k1\_scmfsa\_2)))~(k8\_memstr\_0~np\_\_3~k1\_scmfsa\_2~\\
X3)~(k2\_nat\_1~(k8\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~X0~X1)~\\
(k8\_memstr\_0~np\_\_3~k1\_scmfsa\_2~X3))~np\_\_2))=k2\_nat\_1~(k2\_nat\_1~\\
(k5\_card\_1~X1)~(k5\_card\_1~X2))~np\_\_1){\unicdcdcdhd}((k6\_memstr\_0~np\_\_3~k1\_scmfsa\_2~\\
(k5\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~X0~X1)~(k8\_memstr\_0~\\
np\_\_3~k1\_scmfsa\_2~X3)~(k8\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~\\
X0~X1)~(k8\_memstr\_0~np\_\_3~k1\_scmfsa\_2~X3)))=k6\_memstr\_0~np\_\_3~\\
k1\_scmfsa\_2~(k5\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~X0~(k3\_scmfsa6a~\\
(k3\_scmfsa6a~(k3\_scmfsa6a~X1~(k1\_scmfsa8a~(k2\_nat\_1~(k5\_card\_1~\\
X2)~np\_\_1)))~X2)~(k4\_compos\_1~k1\_scmfsa\_2)))~(k8\_memstr\_0~np\_\_3~\\
k1\_scmfsa\_2~X3)~(k2\_nat\_1~(k8\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~\\
X0~X1)~(k8\_memstr\_0~np\_\_3~k1\_scmfsa\_2~X3))~np\_\_2))){\unicdcdcdhd}(({\unicdcdadad} X4 .  \\
(m2\_subset\_1~X4~k1\_numbers~k5\_numbers){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~(k2\_nat\_1~\\
(k8\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~X0~X1)~(k8\_memstr\_0~\\
np\_\_3~k1\_scmfsa\_2~X3))~np\_\_2)~X4){\unicdcdcdhd}(k3\_extpro\_1~np\_\_3~k1\_scmfsa\_2~\\
(k1\_funct\_4~X0~(k3\_scmfsa6a~(k3\_scmfsa6a~(k3\_scmfsa6a~X1~(k1\_scmfsa8a~\\
(k2\_nat\_1~(k5\_card\_1~X2)~np\_\_1)))~X2)~(k4\_compos\_1~k1\_scmfsa\_2)))~\\
(k5\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~X0~(k3\_scmfsa6a~(k3\_scmfsa6a~\\
(k3\_scmfsa6a~X1~(k1\_scmfsa8a~(k2\_nat\_1~(k5\_card\_1~X2)~np\_\_1)))~\\
X2)~(k4\_compos\_1~k1\_scmfsa\_2)))~(k8\_memstr\_0~np\_\_3~k1\_scmfsa\_2~\\
X3)~X4)=k2\_compos\_1~k1\_scmfsa\_2))){\unicdcdcdhd}(({\unicdcdadad} X4 .  (m2\_subset\_1~\\
X4~k1\_numbers~k5\_numbers){\unicdbdjdcd}((r1\_xxreal\_0~X4~(k8\_extpro\_1~np\_\_3~\\
k1\_scmfsa\_2~(k1\_funct\_4~X0~X1)~(k8\_memstr\_0~np\_\_3~k1\_scmfsa\_2~\\
X3))){\unicdbdjdcd}(k5\_memstr\_0~np\_\_3~k1\_scmfsa\_2~(k5\_extpro\_1~np\_\_3~k1\_scmfsa\_2~\\
(k1\_funct\_4~X0~(k3\_scmfsa6a~(k3\_scmfsa6a~(k3\_scmfsa6a~X1~(k1\_scmfsa8a~\\
(k2\_nat\_1~(k5\_card\_1~X2)~np\_\_1)))~X2)~(k4\_compos\_1~k1\_scmfsa\_2)))~\\
(k8\_memstr\_0~np\_\_3~k1\_scmfsa\_2~X3)~X4)=k5\_memstr\_0~np\_\_3~k1\_scmfsa\_2~\\
(k5\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~X0~X1)~(k8\_memstr\_0~\\
np\_\_3~k1\_scmfsa\_2~X3)~X4)))){\unicdcdcdhd}((k5\_memstr\_0~np\_\_3~k1\_scmfsa\_2~\\
(k5\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~X0~(k3\_scmfsa6a~(k3\_scmfsa6a~\\
(k3\_scmfsa6a~X1~(k1\_scmfsa8a~(k2\_nat\_1~(k5\_card\_1~X2)~np\_\_1)))~\\
X2)~(k4\_compos\_1~k1\_scmfsa\_2)))~(k8\_memstr\_0~np\_\_3~k1\_scmfsa\_2~\\
X3)~(k2\_nat\_1~(k8\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~X0~X1)~\\
(k8\_memstr\_0~np\_\_3~k1\_scmfsa\_2~X3))~np\_\_1))=k5\_card\_1~X1){\unicdcdcdhd}((\\
r1\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~X0~(k3\_scmfsa6a~(k3\_scmfsa6a~\\
(k3\_scmfsa6a~X1~(k1\_scmfsa8a~(k2\_nat\_1~(k5\_card\_1~X2)~np\_\_1)))~\\
X2)~(k4\_compos\_1~k1\_scmfsa\_2)))~(k8\_memstr\_0~np\_\_3~k1\_scmfsa\_2~\\
X3)){\unicdcdcdhd}(k8\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~X0~(k3\_scmfsa6a~\\
(k3\_scmfsa6a~(k3\_scmfsa6a~X1~(k1\_scmfsa8a~(k2\_nat\_1~(k5\_card\_1~\\
X2)~np\_\_1)))~X2)~(k4\_compos\_1~k1\_scmfsa\_2)))~(k8\_memstr\_0~np\_\_3~\\
k1\_scmfsa\_2~X3)=k2\_nat\_1~(k8\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~\\
X0~X1)~(k8\_memstr\_0~np\_\_3~k1\_scmfsa\_2~X3))~np\_\_2)))))))))))\end{array}
\label{hyp:mgedfdpfdhdgngggdhbgidbg}
\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 .  k16\_funcop\_1~X0~X1=k7\_funcop\_1~(k1\_tarski~\\
X0)~X1\end{array}
\label{hyp:egjdpfggfhogdgpgahpfbd}
\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~X0=k1\_funct\_4~X0~(k8\_memstr\_0~np\_\_3~k1\_scmfsa\_2~\\
(k16\_funcop\_1~(k4\_scmfsa\_2~k6\_numbers)~np\_\_1)))\end{array}
\label{hyp:egbdpfdhdgngggdhbgpfng}
\end{equation}
\begin{theorem}\label{thm:mgedidpfdhdgngggdhbgidbg}
$$\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 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_relat\_1~\\
X1){\unicdcdcdhd}((v4\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X1~(u1\_compos\_1~\\
k1\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_finset\_1~X1){\unicdcdcdhd}(v1\_afinsq\_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\_scmfsa\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_finset\_1~X2){\unicdcdcdhd}(v1\_afinsq\_1~X2))))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((v4\_relat\_1~X3~(u1\_struct\_0~k1\_scmfsa\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X3){\unicdcdcdhd}((v5\_funct\_1~X3~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X3~(u1\_struct\_0~k1\_scmfsa\_2)))))){\unicdbdjdcd}(((r5\_scmfsa7b~\\
X1~(k1\_scmfsa\_m~X3)~X0){\unicdcdcdhd}(r6\_scmfsa7b~X1~(k1\_scmfsa\_m~X3)~X0)){\unicdbdjdcd}\\
((k5\_memstr\_0~np\_\_3~k1\_scmfsa\_2~(k5\_extpro\_1~np\_\_3~k1\_scmfsa\_2~\\
(k1\_funct\_4~X0~(k3\_scmfsa6a~(k3\_scmfsa6a~(k3\_scmfsa6a~X1~(k1\_scmfsa8a~\\
(k2\_nat\_1~(k5\_card\_1~X2)~np\_\_1)))~X2)~(k4\_compos\_1~k1\_scmfsa\_2)))~\\
(k1\_funct\_4~X3~(k8\_memstr\_0~np\_\_3~k1\_scmfsa\_2~(k16\_funcop\_1~(\\
k4\_scmfsa\_2~k6\_numbers)~np\_\_1)))~(k2\_nat\_1~(k8\_extpro\_1~np\_\_3~\\
k1\_scmfsa\_2~(k1\_funct\_4~X0~X1)~(k1\_funct\_4~X3~(k8\_memstr\_0~np\_\_3~\\
k1\_scmfsa\_2~(k16\_funcop\_1~(k4\_scmfsa\_2~k6\_numbers)~np\_\_1))))~\\
np\_\_2))=k2\_nat\_1~(k2\_nat\_1~(k5\_card\_1~X1)~(k5\_card\_1~X2))~np\_\_1){\unicdcdcdhd}\\
((k6\_memstr\_0~np\_\_3~k1\_scmfsa\_2~(k5\_extpro\_1~np\_\_3~k1\_scmfsa\_2~\\
(k1\_funct\_4~X0~X1)~(k1\_funct\_4~X3~(k8\_memstr\_0~np\_\_3~k1\_scmfsa\_2~\\
(k16\_funcop\_1~(k4\_scmfsa\_2~k6\_numbers)~np\_\_1)))~(k8\_extpro\_1~\\
np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~X0~X1)~(k1\_funct\_4~X3~(k8\_memstr\_0~\\
np\_\_3~k1\_scmfsa\_2~(k16\_funcop\_1~(k4\_scmfsa\_2~k6\_numbers)~np\_\_1)))))=\\
k6\_memstr\_0~np\_\_3~k1\_scmfsa\_2~(k5\_extpro\_1~np\_\_3~k1\_scmfsa\_2~\\
(k1\_funct\_4~X0~(k3\_scmfsa6a~(k3\_scmfsa6a~(k3\_scmfsa6a~X1~(k1\_scmfsa8a~\\
(k2\_nat\_1~(k5\_card\_1~X2)~np\_\_1)))~X2)~(k4\_compos\_1~k1\_scmfsa\_2)))~\\
(k1\_funct\_4~X3~(k8\_memstr\_0~np\_\_3~k1\_scmfsa\_2~(k16\_funcop\_1~(\\
k4\_scmfsa\_2~k6\_numbers)~np\_\_1)))~(k2\_nat\_1~(k8\_extpro\_1~np\_\_3~\\
k1\_scmfsa\_2~(k1\_funct\_4~X0~X1)~(k1\_funct\_4~X3~(k8\_memstr\_0~np\_\_3~\\
k1\_scmfsa\_2~(k16\_funcop\_1~(k4\_scmfsa\_2~k6\_numbers)~np\_\_1))))~\\
np\_\_2))){\unicdcdcdhd}(({\unicdcdadad} X4 .  (m2\_subset\_1~X4~k1\_numbers~k5\_numbers){\unicdbdjdcd}\\
(\preoh (\preoh r1\_xxreal\_0~(k2\_nat\_1~(k8\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~\\
X0~X1)~(k1\_funct\_4~X3~(k8\_memstr\_0~np\_\_3~k1\_scmfsa\_2~(k16\_funcop\_1~\\
(k4\_scmfsa\_2~k6\_numbers)~np\_\_1))))~np\_\_2)~X4){\unicdcdcdhd}(k3\_extpro\_1~np\_\_3~\\
k1\_scmfsa\_2~(k1\_funct\_4~X0~(k3\_scmfsa6a~(k3\_scmfsa6a~(k3\_scmfsa6a~\\
X1~(k1\_scmfsa8a~(k2\_nat\_1~(k5\_card\_1~X2)~np\_\_1)))~X2)~(k4\_compos\_1~\\
k1\_scmfsa\_2)))~(k5\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~X0~\\
(k3\_scmfsa6a~(k3\_scmfsa6a~(k3\_scmfsa6a~X1~(k1\_scmfsa8a~(k2\_nat\_1~\\
(k5\_card\_1~X2)~np\_\_1)))~X2)~(k4\_compos\_1~k1\_scmfsa\_2)))~(k1\_funct\_4~\\
X3~(k8\_memstr\_0~np\_\_3~k1\_scmfsa\_2~(k16\_funcop\_1~(k4\_scmfsa\_2~\\
k6\_numbers)~np\_\_1)))~X4)=k2\_compos\_1~k1\_scmfsa\_2))){\unicdcdcdhd}(({\unicdcdadad} X4 .  \\
(m2\_subset\_1~X4~k1\_numbers~k5\_numbers){\unicdbdjdcd}((r1\_xxreal\_0~X4~(k8\_extpro\_1~\\
np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~X0~X1)~(k1\_funct\_4~X3~(k8\_memstr\_0~\\
np\_\_3~k1\_scmfsa\_2~(k16\_funcop\_1~(k4\_scmfsa\_2~k6\_numbers)~np\_\_1))))){\unicdbdjdcd}\\
(k5\_memstr\_0~np\_\_3~k1\_scmfsa\_2~(k5\_extpro\_1~np\_\_3~k1\_scmfsa\_2~\\
(k1\_funct\_4~X0~(k3\_scmfsa6a~(k3\_scmfsa6a~(k3\_scmfsa6a~X1~(k1\_scmfsa8a~\\
(k2\_nat\_1~(k5\_card\_1~X2)~np\_\_1)))~X2)~(k4\_compos\_1~k1\_scmfsa\_2)))~\\
(k1\_funct\_4~X3~(k8\_memstr\_0~np\_\_3~k1\_scmfsa\_2~(k16\_funcop\_1~(\\
k4\_scmfsa\_2~k6\_numbers)~np\_\_1)))~X4)=k5\_memstr\_0~np\_\_3~k1\_scmfsa\_2~\\
(k5\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~X0~X1)~(k1\_funct\_4~\\
X3~(k8\_memstr\_0~np\_\_3~k1\_scmfsa\_2~(k16\_funcop\_1~(k4\_scmfsa\_2~\\
k6\_numbers)~np\_\_1)))~X4)))){\unicdcdcdhd}((k5\_memstr\_0~np\_\_3~k1\_scmfsa\_2~\\
(k5\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~X0~(k3\_scmfsa6a~(k3\_scmfsa6a~\\
(k3\_scmfsa6a~X1~(k1\_scmfsa8a~(k2\_nat\_1~(k5\_card\_1~X2)~np\_\_1)))~\\
X2)~(k4\_compos\_1~k1\_scmfsa\_2)))~(k1\_funct\_4~X3~(k8\_memstr\_0~np\_\_3~\\
k1\_scmfsa\_2~(k16\_funcop\_1~(k4\_scmfsa\_2~k6\_numbers)~np\_\_1)))~\\
(k2\_nat\_1~(k8\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~X0~X1)~(k1\_funct\_4~\\
X3~(k8\_memstr\_0~np\_\_3~k1\_scmfsa\_2~(k16\_funcop\_1~(k4\_scmfsa\_2~\\
k6\_numbers)~np\_\_1))))~np\_\_1))=k5\_card\_1~X1){\unicdcdcdhd}((r1\_extpro\_1~np\_\_3~\\
k1\_scmfsa\_2~(k1\_funct\_4~X0~(k3\_scmfsa6a~(k3\_scmfsa6a~(k3\_scmfsa6a~\\
X1~(k1\_scmfsa8a~(k2\_nat\_1~(k5\_card\_1~X2)~np\_\_1)))~X2)~(k4\_compos\_1~\\
k1\_scmfsa\_2)))~(k1\_funct\_4~X3~(k8\_memstr\_0~np\_\_3~k1\_scmfsa\_2~\\
(k16\_funcop\_1~(k4\_scmfsa\_2~k6\_numbers)~np\_\_1)))){\unicdcdcdhd}(k8\_extpro\_1~\\
np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~X0~(k3\_scmfsa6a~(k3\_scmfsa6a~(k3\_scmfsa6a~\\
X1~(k1\_scmfsa8a~(k2\_nat\_1~(k5\_card\_1~X2)~np\_\_1)))~X2)~(k4\_compos\_1~\\
k1\_scmfsa\_2)))~(k1\_funct\_4~X3~(k8\_memstr\_0~np\_\_3~k1\_scmfsa\_2~\\
(k16\_funcop\_1~(k4\_scmfsa\_2~k6\_numbers)~np\_\_1)))=k2\_nat\_1~(k8\_extpro\_1~\\
np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~X0~X1)~(k1\_funct\_4~X3~(k8\_memstr\_0~\\
np\_\_3~k1\_scmfsa\_2~(k16\_funcop\_1~(k4\_scmfsa\_2~k6\_numbers)~np\_\_1))))~\\
np\_\_2)))))))))))\end{array}$$
\end{theorem}
\end{document}
