\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{t101\_finseq\_3 (TMTAryQcwqAztmETqYFFcvk9jBTdptzwtjs)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_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\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ k11\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0{\unicdcdgdad}X1){\unicdcdcdhd}((X1{\unicdcdgdad}X2){\unicdcdcdhd}(X2{\unicdcdgdad}X0))){\unicdbdjded}\\
(v2\_funct\_1~(k11\_finseq\_1~X0~X1~X2))\end{array}
\label{hyp:ehjdfdpfggjgogdhfgbhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v2\_funct\_1~X0){\unicdcdcdhd}((k10\_xtuple\_0~\\
X0=k1\_enumset1~X1~X2~X3){\unicdcdcdhd}(v2\_funct\_1~(k11\_finseq\_1~X1~X2~X3)))){\unicdbdjdcd}\\
(k3\_finseq\_1~X0=np\_\_3))\end{array}
\label{hyp:ehbdadadpfggjgogdhfgbhpfdd}
\end{equation}
\begin{theorem}\label{thm:ehbdadbdpfggjgogdhfgbhpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v2\_funct\_1~X0){\unicdcdcdhd}(k10\_xtuple\_0~\\
X0=k1\_enumset1~X1~X2~X3)){\unicdbdjdcd}((X1=X2){\unicdcdcdid}((X2=X3){\unicdcdcdid}((X1=X3){\unicdcdcdid}(k3\_finseq\_1~\\
X0=np\_\_3)))))\end{array}$$
\end{theorem}
\end{document}
