\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\_funct\_7 (TMFQcMxSiv9rbayEcGUpxRMfCZtp3AkGRL4)}
\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 $ k6\_funct\_7 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_funct\_7 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k5\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~\\
X1))){\unicdbdjdcd}(k1\_funct\_1~(k7\_finseq\_1~X1~(k9\_finseq\_1~X0))~(k2\_nat\_1~\\
(k3\_finseq\_1~X1)~np\_\_1)=X0)\end{array}
\label{hyp:ehedcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~\\
X1))){\unicdbdjdcd}(k1\_funct\_1~(k7\_finseq\_1~(k9\_finseq\_1~X0)~X1)~np\_\_1=X0)\end{array}
\label{hyp:ehedbdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~\\
X1))){\unicdbdjdcd}((X1=k9\_finseq\_1~X0){\unicdbdjded}((k3\_finseq\_1~X1=np\_\_1){\unicdcdcdhd}(k1\_funct\_1~\\
X1~np\_\_1=X0)))\end{array}
\label{hyp:ehedadpfggjgogdhfgbhpfbd}
\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}(k3\_finseq\_1~(k7\_finseq\_1~X0~X1)=k2\_nat\_1~(k3\_finseq\_1~\\
X0)~(k3\_finseq\_1~X1)))\end{array}
\label{hyp:ehcdcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k9\_finseq\_1}~{X0}}={{k5\_finseq\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v1\_finseq\_1}~{({{k5\_finseq\_1}~{X0}})}}}\label{hyp:ggdghdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~(k5\_finseq\_1~X0)){\unicdcdcdhd}(v1\_funct\_1~(k5\_finseq\_1~\\
X0))\end{array}
\label{hyp:ggdggdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~\\
X0))){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(v1\_finseq\_1~X1))))){\unicdbdjdcd}((v1\_relat\_1~(k7\_finseq\_1~X1~X0)){\unicdcdcdhd}((v1\_funct\_1~\\
(k7\_finseq\_1~X1~X0)){\unicdcdcdhd}((\preoh v1\_xboole\_0~(k7\_finseq\_1~X1~X0)){\unicdcdcdhd}(v1\_finseq\_1~\\
(k7\_finseq\_1~X1~X0)))))\end{array}
\label{hyp:ggdgbdidpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~\\
X0))){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(v1\_finseq\_1~X1))))){\unicdbdjdcd}((v1\_relat\_1~(k7\_finseq\_1~X0~X1)){\unicdcdcdhd}((v1\_funct\_1~\\
(k7\_finseq\_1~X0~X1)){\unicdcdcdhd}((\preoh v1\_xboole\_0~(k7\_finseq\_1~X0~X1)){\unicdcdcdhd}(v1\_finseq\_1~\\
(k7\_finseq\_1~X0~X1)))))\end{array}
\label{hyp:ggdgbdhdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {\preoh{{{v1\_xboole\_0}~{({{k5\_finseq\_1}~{X0}})}}}}}\label{hyp:ggdgbdgdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~\\
X0))){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~X1)))){\unicdbdjdcd}\\
((v1\_relat\_1~(k7\_finseq\_1~X0~X1)){\unicdcdcdhd}((v1\_funct\_1~(k7\_finseq\_1~\\
X0~X1)){\unicdcdcdhd}(v1\_finseq\_1~(k7\_finseq\_1~X0~X1))))\end{array}
\label{hyp:egehpflghdpfggjgogdhfgbhpfbd}
\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\_xboole\_0~X0){\unicdbdjdcd}((X1=k7\_funct\_7~X0){\unicdbdjded}(v1\_xboole\_0~\\
X1))){\unicdcdcdhd}((\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((X1=k7\_funct\_7~X0){\unicdbdjded}(X1=k10\_xtuple\_0~\\
(k1\_funct\_1~X0~(k3\_finseq\_1~X0))))))\end{array}
\label{hyp:eghdpfggfhogdgehpfhd}
\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\_xboole\_0~X0){\unicdbdjdcd}((X1=k6\_funct\_7~X0){\unicdbdjded}(v1\_xboole\_0~\\
X1))){\unicdcdcdhd}((\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((X1=k6\_funct\_7~X0){\unicdbdjded}(X1=k9\_xtuple\_0~\\
(k1\_funct\_1~X0~np\_\_1)))))\end{array}
\label{hyp:eggdpfggfhogdgehpfhd}
\end{equation}
\begin{theorem}\label{thm:ehfdidpfggfhogdgehpfhd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~X1))){\unicdbdjdcd}((k6\_funct\_7~\\
(k7\_finseq\_1~(k9\_finseq\_1~X0)~X1)=k9\_xtuple\_0~X0){\unicdcdcdhd}(k7\_funct\_7~\\
(k7\_finseq\_1~X1~(k9\_finseq\_1~X0))=k10\_xtuple\_0~X0)))\end{array}$$
\end{theorem}
\end{document}
