\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{t17\_trees\_9 (TMao1ggELxVDPAq6WndUvAsnLnSv4fgasv3)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_trees\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_trees\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_trees\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_trees\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_trees\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v3\_trees\_2~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  k7\_trees\_9~X0~X1=ReplSep~(toset~({\uniddcgcg} X2 : \iota .  m1\_trees\_1~\\
X2~(k9\_xtuple\_0~X0)))~({\uniddcgcg} X2 : \iota .  \preoh (X2 \in k3\_trees\_1~(k9\_xtuple\_0~\\
X0)){\unicdcdcdhd}(\preoh k1\_funct\_1~X0~X2 \in X1))~({\uniddcgcg} X2 : \iota .  k5\_trees\_2~X0~X2))\end{array}
\label{hyp:egjdpfehchfgfgdhpfjd}
\end{equation}
\begin{theorem}\label{thm:ehbdhdpfehchfgfgdhpfjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v3\_trees\_2~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (X0 \in k7\_trees\_9~X1~X2){\unicdbdjded}({\unicdcdaddd} X3 .  (m1\_trees\_1~\\
X3~(k9\_xtuple\_0~X1)){\unicdcdcdhd}((X0=k5\_trees\_2~X1~X3){\unicdcdcdhd}(\preoh (X3 \in k3\_trees\_1~\\
(k9\_xtuple\_0~X1)){\unicdcdcdhd}(\preoh k1\_funct\_1~X1~X3 \in X2)))))\end{array}$$
\end{theorem}
\end{document}
