\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{t54\_funct\_5 (TMQ1bR2RCK3wRH7TupQwaz8pshXNjFHpifD)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_funct\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k1\_funct\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_funct\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_funct\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~\\
X2)){\unicdbdjdcd}((r1\_tarski~(k10\_xtuple\_0~X2)~(k4\_partfun1~X0~X1)){\unicdbdjdcd}((k1\_xboole\_0 \in \\
k10\_xtuple\_0~X2){\unicdcdcdid}((k1\_funct\_5~(k2\_funct\_5~X2)=X2){\unicdcdcdhd}(k3\_funct\_5~\\
(k4\_funct\_5~X2)=X2))))\end{array}
\label{hyp:ehfdbdpfggfhogdgehpffd}
\end{equation}
\begin{theorem}\label{thm:ehfdedpfggfhogdgehpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~\\
X2)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}(v1\_funct\_1~X3)){\unicdbdjdcd}(((r1\_tarski~\\
(k10\_xtuple\_0~X2)~(k4\_partfun1~X0~X1)){\unicdcdcdhd}((r1\_tarski~(k10\_xtuple\_0~\\
X3)~(k4\_partfun1~X0~X1)){\unicdcdcdhd}(k2\_funct\_5~X2=k2\_funct\_5~X3))){\unicdbdjdcd}((k1\_xboole\_0 \in \\
k10\_xtuple\_0~X2){\unicdcdcdid}((k1\_xboole\_0 \in k10\_xtuple\_0~X3){\unicdcdcdid}(X2=X3)))))\end{array}$$
\end{theorem}
\end{document}
