\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{t8\_scmpds\_2 (TMcjhmD8KMoR5ernkugDbjxrg1ccvQW2pWb)}
\maketitle
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_ami\_2 : {\iota}$ be given.
Let $ k2\_ami\_2 : {\iota}$ be given.
Let $ k3\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k12\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_scmpds\_i : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_scm\_inst : {\iota}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k4\_numbers : {\iota}$ be given.
Let $ np\_\_14 : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k7\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_15 : {\iota}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ k11\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ np\_\_4 : {\iota}$ be given.
Let $ np\_\_5 : {\iota}$ be given.
Let $ np\_\_6 : {\iota}$ be given.
Let $ np\_\_7 : {\iota}$ be given.
Let $ np\_\_8 : {\iota}$ be given.
Let $ k7\_finseq\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ np\_\_9 : {\iota}$ be given.
Let $ np\_\_10 : {\iota}$ be given.
Let $ np\_\_11 : {\iota}$ be given.
Let $ np\_\_12 : {\iota}$ be given.
Let $ np\_\_13 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k2\_ami\_2}={k2\_scm\_inst}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfbgngjgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k2\_scm\_inst}}}}\label{hyp:ggdgbdpfdhdgngpfjgogdheh}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_ami\_2}}}}\label{hyp:ggdgbdpfbgngjgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k2\_ami\_2}}~{({{k1\_zfmisc\_1}~{k1\_ami\_2}})}}\label{hyp:egehpflgcdpfbgngjgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k2\_xboole\_0~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}((X3 \in X0){\unicdcdcdid}(X3 \in X1)))\end{array}
\label{hyp:egddpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k1\_scmpds\_i=k2\_xboole\_0~(k2\_xboole\_0~(k2\_xboole\_0~(k2\_xboole\_0~\\
(k2\_xboole\_0~(k1\_tarski~(k3\_xtuple\_0~k6\_numbers~k1\_xboole\_0~\\
k1\_xboole\_0))~(ReplSep~(toset~({\uniddcgcg} X0 : \iota .  m1\_subset\_1~X0~k4\_numbers))~\\
({\uniddcgcg} X0 : \iota .  True)~({\uniddcgcg} X0 : \iota .  k3\_xtuple\_0~np\_\_14~k1\_xboole\_0~\\
(k12\_finseq\_1~k4\_numbers~X0))))~(ReplSep~(toset~({\uniddcgcg} X0 : \iota .  \\
m1\_subset\_1~X0~k2\_scm\_inst))~({\uniddcgcg} X0 : \iota .  True)~({\uniddcgcg} X0 : \iota .  \\
k3\_xtuple\_0~np\_\_1~k1\_xboole\_0~(k12\_finseq\_1~k2\_scm\_inst~X0))))~\\
(ReplSep3~(toset~({\uniddcgcg} X0 : \iota .  m2\_subset\_1~X0~k4\_ordinal1~(k7\_card\_1~\\
np\_\_15)))~({\uniddcgcg} X0 : \iota .  toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~X1~k2\_scm\_inst))~\\
({\uniddcgcg} X0 : \iota .  {\uniddcgcg} X1 : \iota .  toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~X2~k4\_numbers))~\\
({\uniddcgcg} X0 : \iota .  {\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  X0 \in k2\_tarski~np\_\_2~np\_\_3)~\\
({\uniddcgcg} X0 : \iota .  {\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  k3\_xtuple\_0~X0~k1\_xboole\_0~\\
(k10\_finseq\_1~X1~X2))))~(ReplSep4~(toset~({\uniddcgcg} X0 : \iota .  m2\_subset\_1~\\
X0~k4\_ordinal1~(k7\_card\_1~np\_\_15)))~({\uniddcgcg} X0 : \iota .  toset~({\uniddcgcg} X1 : \\
\iota .  m1\_subset\_1~X1~k2\_scm\_inst))~({\uniddcgcg} X0 : \iota .  {\uniddcgcg} X1 : \iota .  toset~\\
({\uniddcgcg} X2 : \iota .  m1\_subset\_1~X2~k4\_numbers))~({\uniddcgcg} X0 : \iota .  {\uniddcgcg} X1 : \\
\iota .  {\uniddcgcg} X2 : \iota .  toset~({\uniddcgcg} X3 : \iota .  m1\_subset\_1~X3~k4\_numbers))~\\
({\uniddcgcg} X0 : \iota .  {\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  X0 \in k3\_enumset1~\\
np\_\_4~np\_\_5~np\_\_6~np\_\_7~np\_\_8)~({\uniddcgcg} X0 : \iota .  {\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \\
\iota .  {\uniddcgcg} X3 : \iota .  k3\_xtuple\_0~X0~k1\_xboole\_0~(k11\_finseq\_1~X1~X2~\\
X3))))~(ReplSep5~(toset~({\uniddcgcg} X0 : \iota .  m2\_subset\_1~X0~k4\_ordinal1~\\
(k7\_card\_1~np\_\_15)))~({\uniddcgcg} X0 : \iota .  toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~\\
X1~k2\_scm\_inst))~({\uniddcgcg} X0 : \iota .  {\uniddcgcg} X1 : \iota .  toset~({\uniddcgcg} X2 : \iota .  \\
m1\_subset\_1~X2~k2\_scm\_inst))~({\uniddcgcg} X0 : \iota .  {\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \\
\iota .  toset~({\uniddcgcg} X3 : \iota .  m1\_subset\_1~X3~k4\_numbers))~({\uniddcgcg} X0 : \iota .  \\
{\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  toset~({\uniddcgcg} X4 : \iota .  m1\_subset\_1~\\
X4~k4\_numbers))~({\uniddcgcg} X0 : \iota .  {\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \\
\iota .  {\uniddcgcg} X4 : \iota .  X0 \in k3\_enumset1~np\_\_9~np\_\_10~np\_\_11~np\_\_12~np\_\_13)~\\
({\uniddcgcg} X0 : \iota .  {\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  {\uniddcgcg} X4 : \iota .  \\
k3\_xtuple\_0~X0~k1\_xboole\_0~(k7\_finseq\_4~X1~X2~X3~X4)))\end{array}
\label{hyp:egbdpfdhdgngahegdhpfjg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_xboole\_0}~{X0}}~{X1}}={{{k2\_xboole\_0}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehidpfdhdgngahegdhpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_ami\_2~k2\_ami\_2){\unicdbdjdcd}(k3\_xtuple\_0~np\_\_1~\\
k1\_xboole\_0~(k12\_finseq\_1~k2\_ami\_2~X0) \in k1\_scmpds\_i)\end{array}$$
\end{theorem}
\end{document}
