\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{t72\_abcmiz\_1 (TMJtykxsuWhPxEurrsLjyeUoo3qDS2E24r9)}
\maketitle
Let $ v1\_instalg1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m3\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_finset\_1 : {{\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 $ k38\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v9\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k12\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_msafree3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k28\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k39\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}((v3\_abcmiz\_1~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m3\_abcmiz\_1~X1~X0){\unicdbdjded}(X1 \in \\
k39\_abcmiz\_1~X0))\end{array}
\label{hyp:egedddpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}((v3\_abcmiz\_1~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}(k39\_abcmiz\_1~X0=ReplSep2~(toset~({\uniddcgcg} X1 : \\
\iota .  m1\_abcmiz\_1~X1~X0~(k12\_abcmiz\_1~X0)))~({\uniddcgcg} X1 : \iota .  toset~(\\
{\uniddcgcg} X2 : \iota .  (v1\_finset\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k38\_abcmiz\_1~\\
X0)))))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  v9\_abcmiz\_1~X1~X0)~({\uniddcgcg} X1 : \iota .  \\
{\uniddcgcg} X2 : \iota .  k1\_domain\_1~(k1\_zfmisc\_1~(k38\_abcmiz\_1~X0))~(k3\_card\_3~\\
(u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))~X2~X1))\end{array}
\label{hyp:egedcdpfbgcgdgngjgkhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehhdcdpfbgcgdgngjgkhpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_instalg1~X1){\unicdcdcdhd}((v1\_abcmiz\_1~X1){\unicdcdcdhd}(\\
(v3\_abcmiz\_1~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)))){\unicdbdjdcd}((m3\_abcmiz\_1~X0~X1){\unicdbdjded}(\\
{\unicdcdaddd} X2 .  ((v1\_finset\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k38\_abcmiz\_1~\\
X1)))){\unicdcdcdhd}({\unicdcdaddd} X3 .  ((v9\_abcmiz\_1~X3~X1){\unicdcdcdhd}(m1\_abcmiz\_1~X3~X1~(k12\_abcmiz\_1~\\
X1))){\unicdcdcdhd}(X0=k1\_domain\_1~(k1\_zfmisc\_1~(k38\_abcmiz\_1~X1))~(k3\_card\_3~\\
(u3\_msualg\_1~X1~(k1\_msafree3~X1~(k28\_abcmiz\_1~X1))))~X2~X3))))\end{array}$$
\end{theorem}
\end{document}
