\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{t58\_finseq\_5 (TMYhhS1wfs86weuzqP3Gzfzy1qAqGeJxvSp)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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 $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_finseq\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k10\_xtuple\_0 : {{\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}(v1\_finseq\_1~X0))){\unicdbdjdcd}\\
((k4\_finseq\_1~X0=k4\_finseq\_1~(k3\_finseq\_5~X0)){\unicdcdcdhd}(k10\_xtuple\_0~\\
X0=k10\_xtuple\_0~(k3\_finseq\_5~X0)))\end{array}
\label{hyp:ehfdhdpfggjgogdhfgbhpffd}
\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}\\
((v1\_relat\_1~(k3\_finseq\_5~X0)){\unicdcdcdhd}((v1\_funct\_1~(k3\_finseq\_5~X0)){\unicdcdcdhd}\\
(v1\_finseq\_1~(k3\_finseq\_5~X0))))\end{array}
\label{hyp:egehpflgddpfggjgogdhfgbhpffd}
\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 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~\\
X1))){\unicdbdjdcd}((X1=k3\_finseq\_5~X0){\unicdbdjded}((k3\_finseq\_1~X1=k3\_finseq\_1~X0){\unicdcdcdhd}\\
({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}((X2 \in k4\_finseq\_1~X1){\unicdbdjdcd}(k1\_funct\_1~\\
X1~X2=k1\_funct\_1~X0~(k2\_xcmplx\_0~(k6\_xcmplx\_0~(k3\_finseq\_1~X0)~\\
X2)~np\_\_1)))))))\end{array}
\label{hyp:egddpfggjgogdhfgbhpffd}
\end{equation}
\begin{theorem}\label{thm:ehfdidpfggjgogdhfgbhpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((\\
v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~X1))){\unicdbdjdcd}((X0 \in k4\_finseq\_1~X1){\unicdbdjdcd}(k1\_funct\_1~\\
(k3\_finseq\_5~X1)~X0=k1\_funct\_1~X1~(k2\_xcmplx\_0~(k6\_xcmplx\_0~(\\
k3\_finseq\_1~X1)~X0)~np\_\_1))))\end{array}$$
\end{theorem}
\end{document}
