\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{t114\_scmpds\_6 (TMGqFeBb6JZvKKfqH6t98C5i6MFgETUjhxV)}
\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 $ 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 $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\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\_scmpds\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_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 $ k7\_scmpds\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_funct\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_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 $ np\_\_1 : {\iota}$ be given.
Let $ k5\_scmpds\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ 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\_ami\_2~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(\\
u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X5 .  (v1\_int\_1~X5){\unicdbdjdcd}((r1\_xxreal\_0~\\
(k1\_funct\_1~X1~(k2\_scmpds\_2~(k1\_funct\_1~X1~X3)~X5))~k6\_numbers){\unicdbdjdcd}\\
(k1\_funct\_1~(k6\_scmpds\_4~(k7\_scmpds\_6~X3~X5~X2)~(k8\_memstr\_0~np\_\_2~\\
k1\_scmpds\_2~X1)~X0)~X4=k1\_funct\_1~X1~X4)))))))\end{array}
\label{hyp:ehidedpfdhdgngahegdhpfgd}
\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))))))){\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\_xxreal\_0~(k1\_funct\_1~\\
X1~(k2\_scmpds\_2~(k1\_funct\_1~X1~X3)~X4))~k6\_numbers){\unicdbdjdcd}(k6\_scmpds\_4~\\
(k7\_scmpds\_6~X3~X4~X2)~(k8\_memstr\_0~np\_\_2~k1\_scmpds\_2~X1)~X0=k1\_funct\_4~\\
X1~(k7\_memstr\_0~np\_\_2~k1\_scmpds\_2~(k2\_nat\_1~(k5\_card\_1~X2)~np\_\_1))))))))\end{array}
\label{hyp:ehidbdpfdhdgngahegdhpfgd}
\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))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_ami\_2~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(u1\_struct\_0~\\
k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_ami\_2~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(\\
u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X5 .  (v1\_int\_1~X5){\unicdbdjdcd}((k1\_funct\_1~\\
X1~(k2\_scmpds\_2~(k1\_funct\_1~X1~X3)~X5){\unicdcdgdad}k6\_numbers){\unicdbdjdcd}(k1\_funct\_1~\\
(k6\_scmpds\_4~(k5\_scmpds\_6~X3~X5~X2)~(k8\_memstr\_0~np\_\_2~k1\_scmpds\_2~\\
X1)~X0)~X4=k1\_funct\_1~X1~X4)))))))\end{array}
\label{hyp:ehfdedpfdhdgngahegdhpfgd}
\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))))))){\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){\unicdcdgdad}k6\_numbers){\unicdbdjdcd}(k6\_scmpds\_4~(k5\_scmpds\_6~\\
X3~X4~X2)~(k8\_memstr\_0~np\_\_2~k1\_scmpds\_2~X1)~X0=k1\_funct\_4~X1~(k7\_memstr\_0~\\
np\_\_2~k1\_scmpds\_2~(k2\_nat\_1~(k5\_card\_1~X2)~np\_\_1))))))))\end{array}
\label{hyp:ehfdbdpfdhdgngahegdhpfgd}
\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))))))){\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\_xxreal\_0~k6\_numbers~\\
(k1\_funct\_1~X1~(k2\_scmpds\_2~(k1\_funct\_1~X1~X3)~X4))){\unicdbdjdcd}(k6\_scmpds\_4~\\
(k9\_scmpds\_6~X3~X4~X2)~(k8\_memstr\_0~np\_\_2~k1\_scmpds\_2~X1)~X0=k1\_funct\_4~\\
X1~(k7\_memstr\_0~np\_\_2~k1\_scmpds\_2~(k2\_nat\_1~(k5\_card\_1~X2)~np\_\_1))))))))\end{array}
\label{hyp:ehbdbdbdpfdhdgngahegdhpfgd}
\end{equation}
\begin{theorem}\label{thm:ehbdbdedpfdhdgngahegdhpfgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~\\
X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_partfun1~\\
X0~k5\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_funct\_1~\\
X1~(k2\_memstr\_0~np\_\_2~k1\_scmpds\_2)){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~\\
k1\_scmpds\_2)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X2~(u1\_compos\_1~\\
k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_finset\_1~X2){\unicdcdcdhd}(v1\_afinsq\_1~\\
X2))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_ami\_2~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(u1\_struct\_0~\\
k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_ami\_2~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(\\
u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X5 .  (v1\_int\_1~X5){\unicdbdjdcd}((r1\_xxreal\_0~\\
k6\_numbers~(k1\_funct\_1~X1~(k2\_scmpds\_2~(k1\_funct\_1~X1~X3)~X5))){\unicdbdjdcd}\\
(k1\_funct\_1~(k6\_scmpds\_4~(k9\_scmpds\_6~X3~X5~X2)~(k8\_memstr\_0~np\_\_2~\\
k1\_scmpds\_2~X1)~X0)~X4=k1\_funct\_1~X1~X4)))))))\end{array}$$
\end{theorem}
\end{document}
