\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{t2\_scm\_1 (TMSXJqH6sJhWUZrdBBmgiVpew3XAQiYDeAG)}
\maketitle
Let $ v1\_int\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v5\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k1\_ami\_3 : {\iota}$ be given.
Let $ m1\_scm\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_ami\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_0 : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_numbers : {\iota}$ be given.
Let $ v4\_relat\_1 : {{\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 $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v5\_ordinal1~\\
X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_finset\_1~X2)))){\unicdbdjdcd}((X2=k6\_afinsq\_1~\\
X0~X1){\unicdbdjded}((k1\_afinsq\_1~X2=np\_\_2){\unicdcdcdhd}((k1\_funct\_1~X2~k6\_numbers=X0){\unicdcdcdhd}\\
(k1\_funct\_1~X2~np\_\_1=X1))))\end{array}
\label{hyp:ehddidpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(m2\_subset\_1~np\_\_0~k1\_numbers~k5\_numbers){\unicdcdcdhd}((m1\_subset\_1~np\_\_0~\\
k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_0~k1\_numbers))\end{array}
\label{hyp:dhahdgadpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{np\_\_0}}\label{hyp:dhahdgadpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_2}}~{np\_\_1}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchcdpfchbd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_2}}~{np\_\_0}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchcdpfchad}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_relat\_1~(k6\_afinsq\_1~X0~X1)){\unicdcdcdhd}(v1\_funct\_1~\\
(k6\_afinsq\_1~X0~X1))\end{array}
\label{hyp:ggdgjdpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_int\_1~X0){\unicdcdcdhd}(v1\_int\_1~X1)){\unicdbdjdcd}(v5\_relat\_1~\\
(k6\_afinsq\_1~X0~X1)~k4\_numbers)\end{array}
\label{hyp:ggdgcdpfdhdgngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v5\_ordinal1~(k6\_afinsq\_1~X0~X1)){\unicdcdcdhd}(v1\_finset\_1~\\
(k6\_afinsq\_1~X0~X1))\end{array}
\label{hyp:ggdgbdbdpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v5\_relat\_1~X0~k4\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v5\_ordinal1~X0){\unicdcdcdhd}(v1\_finset\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_scm\_1~\\
X1~X0){\unicdbdjdcd}((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~(u1\_struct\_0~k1\_ami\_3)){\unicdcdcdhd}\\
((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_funct\_1~X1~(k2\_memstr\_0~np\_\_2~k1\_ami\_3)){\unicdcdcdhd}\\
(v1\_partfun1~X1~(u1\_struct\_0~k1\_ami\_3)))))))\end{array}
\label{hyp:egehpfngbdpfdhdgngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v5\_relat\_1~X0~k4\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v5\_ordinal1~X0){\unicdcdcdhd}(v1\_finset\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~\\
X1){\unicdcdcdhd}((v4\_relat\_1~X1~(u1\_struct\_0~k1\_ami\_3)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}\\
((v5\_funct\_1~X1~(k2\_memstr\_0~np\_\_2~k1\_ami\_3)){\unicdcdcdhd}(v1\_partfun1~X1~\\
(u1\_struct\_0~k1\_ami\_3)))))){\unicdbdjdcd}((m1\_scm\_1~X1~X0){\unicdbdjded}({\unicdcdadad} X2 .  (\\
m2\_subset\_1~X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}((\preoh r1\_xxreal\_0~(k1\_afinsq\_1~\\
X0)~X2){\unicdbdjdcd}(k1\_funct\_1~X1~(k10\_ami\_3~X2)=k1\_funct\_1~X0~X2)))))\end{array}
\label{hyp:egbdpfdhdgngpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdpfdhdgngpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_int\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m2\_subset\_1~X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v5\_memstr\_0~\\
X3~np\_\_2~k1\_ami\_3~X2){\unicdcdcdhd}(m1\_scm\_1~X3~(k6\_afinsq\_1~X0~X1))){\unicdbdjdcd}((k1\_funct\_1~\\
X3~(k10\_ami\_3~k6\_numbers)=X0){\unicdcdcdhd}(k1\_funct\_1~X3~(k10\_ami\_3~np\_\_1)=\\
X1)))))\end{array}$$
\end{theorem}
\end{document}
