\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{t12\_finseq\_4 (TMHkoR1UFYKMKaXDhfgHKvN4EYDZoHNKP2b)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_funct\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_finseq\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r2\_finseq\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_xtuple\_0 : {{\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 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}((v2\_funct\_1~X0){\unicdbdjded}\\
({\unicdcdadad} X1 .  (X1 \in k10\_xtuple\_0~X0){\unicdbdjdcd}(r2\_finseq\_4~X0~X1)))\end{array}
\label{hyp:ehidpfggjgogdhfgbhpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}(((\\
v2\_funct\_1~X1){\unicdcdcdhd}(X0 \in k9\_xtuple\_0~X1)){\unicdbdjdcd}((X0=k1\_funct\_1~(k2\_funct\_1~\\
X1)~(k1\_funct\_1~X1~X0)){\unicdcdcdhd}(X0=k1\_funct\_1~(k3\_relat\_1~X1~(k2\_funct\_1~\\
X1))~X0)))\end{array}
\label{hyp:ehddedpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (r2\_finseq\_4~\\
X0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (X2=k1\_finseq\_4~X0~X1){\unicdbdjded}((X2 \in k9\_xtuple\_0~X0){\unicdcdcdhd}\\
(k1\_funct\_1~X0~X2=X1))))\end{array}
\label{hyp:egddpfggjgogdhfgbhpfed}
\end{equation}
\begin{theorem}\label{thm:ehbdcdpfggjgogdhfgbhpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
v2\_funct\_1~X0){\unicdcdcdhd}(X1 \in k10\_xtuple\_0~X0)){\unicdbdjdcd}(k1\_funct\_1~(k2\_funct\_1~\\
X0)~X1=k1\_finseq\_4~X0~X1))\end{array}$$
\end{theorem}
\end{document}
