\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{t19\_afproj (TMNXKZ2JMJy7x9U9emr4iLswAnztrxj1kF7)}
\maketitle
Let $ v7\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_diraf : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_analoaf : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_afproj : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_afproj : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_aff\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (X1 \in k8\_afproj~X0){\unicdbdjded}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdcdcdhd}((X1=k6\_afproj~X0~X2){\unicdcdcdhd}(v1\_aff\_4~X2~X0))))\end{array}
\label{hyp:ehbdfdpfbgggahchpgkg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (k4\_tarski~X0~X1 \in \\
k2\_zfmisc\_1~X2~(k1\_tarski~X3)){\unicdbdjded}((X0 \in X2){\unicdcdcdhd}(X1=X3))\end{array}
\label{hyp:ehbdadgdpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k2\_zfmisc\_1~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}({\unicdcdaddd} X4 .  {\unicdcdaddd} X5 .  (X4 \in X0){\unicdcdcdhd}((X5 \in X1){\unicdcdcdhd}(X3=k4\_tarski~\\
X4~X5))))\end{array}
\label{hyp:egcdpfkhggngjgdhdgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdjdpfbgggahchpgkg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (X1 \in k2\_zfmisc\_1~(k8\_afproj~X0)~(k1\_tarski~np\_\_2)){\unicdbdjded}\\
({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdcdcdhd}\\
((X1=k4\_tarski~(k6\_afproj~X0~X2)~np\_\_2){\unicdcdcdhd}(v1\_aff\_4~X2~X0))))\end{array}$$
\end{theorem}
\end{document}
