\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{t18\_amistd\_1 (TMK1w5rayBoW77qVTiRD5Ac6tV3a8qaYsbQ)}
\maketitle
Let $ v1\_setfam\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_compos\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_compos\_1 : {\iota}$ be given.
Let $ v13\_struct\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_compos\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_compos\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ u2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k16\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u2\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_partfun1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_compos\_1)){\unicdbdjdcd}(k2\_compos\_0~\\
(u1\_compos\_1~k1\_compos\_1)~X0=k6\_numbers)\end{array}
\label{hyp:ehcdpfdgpgngahpgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_setfam\_1~X0){\unicdbdjdcd}((v13\_struct\_0~(k1\_extpro\_1~X0)~\\
np\_\_1){\unicdcdcdhd}(v1\_extpro\_1~(k1\_extpro\_1~X0)~X0))\end{array}
\label{hyp:ggdgbdpffgihehahchpgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_setfam\_1~X0){\unicdbdjdcd}((v1\_extpro\_1~(k1\_extpro\_1~X0)~\\
X0){\unicdcdcdhd}(l1\_extpro\_1~(k1\_extpro\_1~X0)~X0))\end{array}
\label{hyp:egehpflgbdpffgihehahchpgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{({{v1\_compos\_1}~{k1\_compos\_1}})}{\unicdcdcdhd}{({{l1\_compos\_1}~{k1\_compos\_1}})}}\label{hyp:egehpflgbdpfdgpgngahpgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_compos\_1~X0){\unicdcdcdhd}(l1\_compos\_1~X0)){\unicdbdjdcd}((X0=k1\_compos\_1){\unicdbdjded}\\
(u1\_compos\_1~X0=k1\_tarski~(k3\_xtuple\_0~k6\_numbers~k1\_xboole\_0~\\
k1\_xboole\_0)))\end{array}
\label{hyp:egidpfdgpgngahpgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_setfam\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_extpro\_1~X1~X0){\unicdcdcdhd}\\
(l1\_extpro\_1~X1~X0)){\unicdbdjdcd}((X1=k1\_extpro\_1~X0){\unicdbdjded}((u1\_struct\_0~X1=\\
k6\_domain\_1~k5\_numbers~k6\_numbers){\unicdcdcdhd}((u2\_struct\_0~X1=k6\_numbers){\unicdcdcdhd}\\
((u1\_compos\_1~X1=k1\_tarski~(k3\_xtuple\_0~k6\_numbers~k1\_xboole\_0~\\
k1\_xboole\_0)){\unicdcdcdhd}((u1\_memstr\_0~X0~X1=k16\_funcop\_1~k6\_numbers~k6\_numbers){\unicdcdcdhd}\\
((u2\_memstr\_0~X0~X1=k7\_funcop\_1~X0~k5\_numbers){\unicdcdcdhd}(u1\_extpro\_1~\\
X0~X1=k16\_funcop\_1~(k3\_xtuple\_0~k6\_numbers~k1\_xboole\_0~k1\_xboole\_0)~\\
(k6\_partfun1~(k4\_card\_3~(k3\_relat\_1~(k16\_funcop\_1~k6\_numbers~\\
k6\_numbers)~(k7\_funcop\_1~X0~k5\_numbers))))))))))))\end{array}
\label{hyp:egbdpffgihehahchpgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdidpfbgngjgdhehegpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_setfam\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_compos\_1~\\
(k1\_extpro\_1~X0))){\unicdbdjdcd}(k2\_compos\_0~(u1\_compos\_1~(k1\_extpro\_1~X0))~\\
X1=k6\_numbers))\end{array}$$
\end{theorem}
\end{document}
