\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{t42\_scmpds\_5 (TMFHKaD2f4nmgLru6k5qkqabCqRTF6GLqsz)}
\maketitle
Let $ v1\_ami\_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 $ k1\_scmpds\_2 : {\iota}$ be given.
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 $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ 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 $ v5\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v6\_compos\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_scmpds\_5 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_scmpds\_4 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_scmpds\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_scmpds\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\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 $ k3\_scmpds\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_compos\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ l1\_compos\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k16\_funcop\_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.
Let $ k1\_scmpds\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
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\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}((\\
v5\_relat\_1~X1~(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(\\
v1\_partfun1~X1~k5\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}\\
((v4\_relat\_1~X2~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}\\
((v5\_funct\_1~X2~(k2\_memstr\_0~np\_\_2~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_partfun1~\\
X2~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}(v5\_memstr\_0~X2~np\_\_2~k1\_scmpds\_2~\\
k6\_numbers)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}((v1\_relat\_1~\\
X3){\unicdcdcdhd}((v4\_relat\_1~X3~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X3~(u1\_compos\_1~\\
k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_finset\_1~X3){\unicdcdcdhd}((v1\_afinsq\_1~\\
X3){\unicdcdcdhd}((v2\_compos\_1~X3~k1\_scmpds\_2){\unicdcdcdhd}(v2\_scmpds\_4~X3))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  ((v4\_scmpds\_4~X4){\unicdcdcdhd}((v1\_scmpds\_5~X4){\unicdcdcdhd}(m1\_subset\_1~\\
X4~(u1\_compos\_1~k1\_scmpds\_2)))){\unicdbdjdcd}(k1\_funct\_1~(k6\_scmpds\_4~(k3\_scmpds\_4~\\
X3~X4)~X2~X1)~X0=k1\_funct\_1~(k2\_extpro\_1~np\_\_2~k1\_scmpds\_2~X4~(k6\_scmpds\_4~\\
X3~X2~X1))~X0)))))\end{array}
\label{hyp:ehedbdpfdhdgngahegdhpffd}
\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)){\unicdcdcdhd}(v5\_memstr\_0~X1~np\_\_2~k1\_scmpds\_2~k6\_numbers)))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_scmpds\_5~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_compos\_1~k1\_scmpds\_2))){\unicdbdjdcd}\\
(k2\_extpro\_1~np\_\_2~k1\_scmpds\_2~X2~X1=k6\_scmpds\_4~(k9\_compos\_1~\\
k1\_scmpds\_2~X2)~X1~X0)))\end{array}
\label{hyp:ehedadpfdhdgngahegdhpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_compos\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_compos\_1~\\
X0))){\unicdbdjdcd}(k9\_compos\_1~X0~X1=k3\_afinsq\_1~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfdgpgngahpgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {\preoh{{{v1\_xboole\_0}~{({{k3\_afinsq\_1}~{X0}})}}}}}\label{hyp:ggdgddpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v6\_compos\_0~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(u1\_compos\_1~k1\_scmpds\_2))){\unicdbdjdcd}(v2\_compos\_1~(k3\_afinsq\_1~X0)~\\
k1\_scmpds\_2)\end{array}
\label{hyp:ggdgcdfdpfdhdgngahegdhpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_scmpds\_5~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmpds\_2))){\unicdbdjdcd}\\
((\preoh v1\_xboole\_0~(k3\_afinsq\_1~X0)){\unicdcdcdhd}((v1\_relat\_1~(k3\_afinsq\_1~\\
X0)){\unicdcdcdhd}((v4\_relat\_1~(k3\_afinsq\_1~X0)~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~\\
(k3\_afinsq\_1~X0)~(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~(k3\_afinsq\_1~\\
X0)){\unicdcdcdhd}((v1\_finset\_1~(k3\_afinsq\_1~X0)){\unicdcdcdhd}((v1\_afinsq\_1~(k3\_afinsq\_1~\\
X0)){\unicdcdcdhd}(v2\_scmpds\_4~(k3\_afinsq\_1~X0)))))))))\end{array}
\label{hyp:ggdgbdfdpfdhdgngahegdhpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (l1\_extpro\_1~X1~X0){\unicdbdjdcd}((l1\_memstr\_0~X1~X0){\unicdcdcdhd}\\
(l1\_compos\_1~X1))\end{array}
\label{hyp:egehpfmgbdpffgihehahchpgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{({{{v1\_extpro\_1}~{k1\_scmpds\_2}}~{np\_\_2}})}{\unicdcdcdhd}{({{{l1\_extpro\_1}~{k1\_scmpds\_2}}~{np\_\_2}})}}\label{hyp:egehpflgbdpfdhdgngahegdhpfcd}
\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 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_compos\_1~k1\_scmpds\_2)){\unicdbdjdcd}(k4\_scmpds\_4~X0~X1=\\
k1\_scmpds\_4~(k9\_compos\_1~k1\_scmpds\_2~X0)~(k9\_compos\_1~k1\_scmpds\_2~\\
X1)))\end{array}
\label{hyp:egedpfdhdgngahegdhpfed}
\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}(\\
{\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_compos\_1~k1\_scmpds\_2)){\unicdbdjdcd}(k3\_scmpds\_4~\\
X0~X1=k1\_scmpds\_4~X0~(k9\_compos\_1~k1\_scmpds\_2~X1)))\end{array}
\label{hyp:egddpfdhdgngahegdhpfed}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k3\_afinsq\_1}~{X0}}={{{k16\_funcop\_1}~{k6\_numbers}}~{X0}}}}\label{hyp:egbdpfbgggjgogdhbhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedcdpfdhdgngahegdhpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}((\\
v5\_relat\_1~X1~(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(\\
v1\_partfun1~X1~k5\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}\\
((v4\_relat\_1~X2~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}\\
((v5\_funct\_1~X2~(k2\_memstr\_0~np\_\_2~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_partfun1~\\
X2~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}(v5\_memstr\_0~X2~np\_\_2~k1\_scmpds\_2~\\
k6\_numbers)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v6\_compos\_0~X3~(u1\_compos\_1~\\
k1\_scmpds\_2)){\unicdcdcdhd}((v1\_scmpds\_5~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(u1\_compos\_1~\\
k1\_scmpds\_2)))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v4\_scmpds\_4~X4){\unicdcdcdhd}((v1\_scmpds\_5~\\
X4){\unicdcdcdhd}(m1\_subset\_1~X4~(u1\_compos\_1~k1\_scmpds\_2)))){\unicdbdjdcd}(k1\_funct\_1~\\
(k6\_scmpds\_4~(k4\_scmpds\_4~X3~X4)~X2~X1)~X0=k1\_funct\_1~(k2\_extpro\_1~\\
np\_\_2~k1\_scmpds\_2~X4~(k2\_extpro\_1~np\_\_2~k1\_scmpds\_2~X3~X2))~X0)))))\end{array}$$
\end{theorem}
\end{document}
