\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{t9\_scmfsa\_i (TMNXZozXzigVdTJSavTThPThfFwaL86d3zY)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_compos\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_scmfsa\_i : {\iota}$ be given.
Let $ np\_\_11 : {\iota}$ be given.
Let $ np\_\_12 : {\iota}$ be given.
Let $ k3\_compos\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_compos\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_compos\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_scm\_inst : {\iota}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k7\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_13 : {\iota}$ be given.
Let $ k2\_scm\_inst : {\iota}$ be given.
Let $ k1\_scmfsa\_i : {\iota}$ be given.
Let $ k3\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k11\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_9 : {\iota}$ be given.
Let $ np\_\_10 : {\iota}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}(\preoh (X0{\unicdcdgdad}k1\_tarski~k1\_xboole\_0){\unicdcdcdhd}\\
((k1\_xboole\_0 \in X0){\unicdcdcdhd}({\unicdcdadad} X1 .  \preoh (X1 \in X0){\unicdcdcdhd}(X1{\unicdcdgdad}k1\_xboole\_0))))\end{array}
\label{hyp:mgedfdpfigfgjhehjgoghgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_scmfsa\_i){\unicdbdjdcd}(((k2\_compos\_0~k2\_scmfsa\_i~\\
X0=np\_\_11){\unicdcdcdid}(k2\_compos\_0~k2\_scmfsa\_i~X0=np\_\_12)){\unicdbdjdcd}(k5\_xtuple\_0~\\
X0=k1\_xboole\_0))\end{array}
\label{hyp:mgbdjdpfdhdgngggdhbgpfjg}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k2\_scmfsa\_i}}}})}{\unicdcdcdhd}{({{v1\_compos\_0}~{k2\_scmfsa\_i}})}}\label{hyp:ggdgddpfdhdgngggdhbgpfjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_compos\_0~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_compos\_0~X0))){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k3\_compos\_0~\\
X0~X1)){\unicdcdcdhd}(v4\_funct\_1~(k3\_compos\_0~X0~X1)))\end{array}
\label{hyp:ggdgbdadpfdgpgngahpgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k2\_scmfsa\_i}}}}\label{hyp:egehpflgcdpfdhdgngggdhbgpfjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_compos\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_compos\_0~X0)){\unicdbdjdcd}(k3\_compos\_0~X0~X1=ReplSep~\\
(toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~X2~X0))~({\uniddcgcg} X2 : \iota .  k2\_compos\_0~\\
X0~X2=X1)~({\uniddcgcg} X2 : \iota .  k5\_xtuple\_0~X2)))\end{array}
\label{hyp:egddpfdgpgngahpgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k2\_scmfsa\_i=k2\_xboole\_0~(k2\_xboole\_0~k3\_scm\_inst~(ReplSep4~\\
(toset~({\uniddcgcg} X0 : \iota .  m2\_subset\_1~X0~k4\_ordinal1~(k7\_card\_1~np\_\_13)))~\\
({\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~k1\_scmfsa\_i))~({\uniddcgcg} X0 : \iota .  {\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \\
\iota .  X0 \in k2\_tarski~np\_\_9~np\_\_10)~({\uniddcgcg} X0 : \iota .  {\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \\
\iota .  {\uniddcgcg} X3 : \iota .  k3\_xtuple\_0~X0~k1\_xboole\_0~(k11\_finseq\_1~X1~X3~\\
X2))))~(ReplSep3~(toset~({\uniddcgcg} X0 : \iota .  m2\_subset\_1~X0~k4\_ordinal1~\\
(k7\_card\_1~np\_\_13)))~({\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~k1\_scmfsa\_i))~({\uniddcgcg} X0 : \iota .  {\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \\
\iota .  X0 \in k2\_tarski~np\_\_11~np\_\_12)~({\uniddcgcg} X0 : \iota .  {\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \\
\iota .  k3\_xtuple\_0~X0~k1\_xboole\_0~(k10\_finseq\_1~X1~X2)))\end{array}
\label{hyp:egcdpfdhdgngggdhbgpfjg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjded}{({{\unicdcdadad} X1 .  {\preoh{{{X1} \in {X0}}}}})}}}\label{hyp:egbdpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehjdpfdhdgngggdhbgpfjg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_compos\_0~k2\_scmfsa\_i)){\unicdbdjdcd}(((X0=\\
np\_\_11){\unicdcdcdid}(X0=np\_\_12)){\unicdbdjdcd}(k3\_compos\_0~k2\_scmfsa\_i~X0=k1\_tarski~\\
k1\_xboole\_0))\end{array}$$
\end{theorem}
\end{document}
