\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{l4\_rewrite1 (TMZ67AToVjA3ESvLVa7zCWnphDZVnDN3mg1)}
\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 $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k1\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k16\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{\preoh{{({{X0} \in {X1}})}}}{\unicdcdcdhd}{({{v1\_xboole\_0}~{X1}})}}}}\label{hyp:ehhdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}(v1\_finseq\_1~X0)))){\unicdbdjdcd}((np\_\_1 \in k4\_finseq\_1~X0){\unicdcdcdhd}(k3\_finseq\_1~\\
X0 \in k4\_finseq\_1~X0))\end{array}
\label{hyp:ehgdpfggjgogdhfgbhpffd}
\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}((r1\_tarski~X0~X1){\unicdbdjdcd}(r1\_xxreal\_0~(k3\_finseq\_1~X0)~(k3\_finseq\_1~\\
X1))))\end{array}
\label{hyp:ehgdddpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((\\
r1\_xxreal\_0~X0~X1){\unicdbdjded}(r1\_tarski~(k2\_finseq\_1~X0)~(k2\_finseq\_1~X1))))\end{array}
\label{hyp:ehfdpfggjgogdhfgbhpfbd}
\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 .  (v7\_ordinal1~X1){\unicdbdjdcd}((k5\_relat\_1~X0~(k2\_finseq\_1~X1)=\\
X0){\unicdbdjded}(r1\_xxreal\_0~(k3\_finseq\_1~X0)~X1)))\end{array}
\label{hyp:ehedjdpfggjgogdhfgbhpfdd}
\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}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_finseq\_1~\\
X2))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}(v1\_finseq\_1~\\
X3))){\unicdbdjdcd}(\preoh (k7\_finseq\_1~X0~X1=k7\_finseq\_1~X2~X3){\unicdcdcdhd}((r1\_xxreal\_0~\\
(k3\_finseq\_1~X0)~(k3\_finseq\_1~X2)){\unicdcdcdhd}({\unicdcdadad} X4 .  ((v1\_relat\_1~\\
X4){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}(v1\_finseq\_1~X4))){\unicdbdjdcd}(k7\_finseq\_1~X0~X4{\unicdcdgdad}\\
X2)))))))\end{array}
\label{hyp:ehedhdpfggjgogdhfgbhpfbd}
\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}((r1\_xxreal\_0~(k3\_finseq\_1~X0)~(k3\_finseq\_1~X1)){\unicdbdjded}(r1\_tarski~\\
(k1\_relset\_1~k5\_numbers~X0)~(k1\_relset\_1~k5\_numbers~X1))))\end{array}
\label{hyp:ehddadpfggjgogdhfgbhpfdd}
\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}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_finseq\_1~\\
X2))){\unicdbdjdcd}(\preoh (X0 \in k4\_finseq\_1~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}(\\
\preoh (X3=X0){\unicdcdcdhd}(k2\_nat\_1~(k3\_finseq\_1~X2)~X3 \in k4\_finseq\_1~(k7\_finseq\_1~\\
X2~X1))))))\end{array}
\label{hyp:ehcdhdpfggjgogdhfgbhpfbd}
\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}\\
((X0{\unicdcdgdad}k1\_xboole\_0){\unicdbdjded}(r1\_xxreal\_0~np\_\_1~(k3\_finseq\_1~X0)))\end{array}
\label{hyp:ehcdadpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((\\
X0 \in k2\_finseq\_1~X1){\unicdbdjded}((r1\_xxreal\_0~np\_\_1~X0){\unicdcdcdhd}(r1\_xxreal\_0~X0~X1))))\end{array}
\label{hyp:ehbdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\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}({\unicdcdadad} X2 .  ((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_finseq\_1~X2))){\unicdbdjdcd}(((r1\_xxreal\_0~X0~(\\
k3\_finseq\_1~X1)){\unicdcdcdhd}(X2=k5\_relat\_1~X1~(k2\_finseq\_1~X0))){\unicdbdjdcd}((k3\_finseq\_1~\\
X2=X0){\unicdcdcdhd}(k4\_finseq\_1~X2=k2\_finseq\_1~X0)))))\end{array}
\label{hyp:ehbdhdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((\preoh r1\_xxreal\_0~np\_\_1~X0){\unicdbdjdcd}(X0=k6\_numbers))\end{array}
\label{hyp:ehbdedpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((\\
\preoh r1\_xxreal\_0~(k1\_nat\_1~X1~np\_\_1)~X0){\unicdbdjded}(r1\_xxreal\_0~X0~X1)))\end{array}
\label{hyp:ehbdddpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\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}((((r1\_xxreal\_0~np\_\_1~X0){\unicdcdcdhd}\\
(r1\_xxreal\_0~(k1\_nat\_1~X0~np\_\_1)~(k3\_finseq\_1~X1))){\unicdbdjdcd}((X0 \in k4\_finseq\_1~\\
X1){\unicdcdcdhd}(k1\_nat\_1~X0~np\_\_1 \in k4\_finseq\_1~X1))){\unicdcdcdhd}(((X0 \in k4\_finseq\_1~\\
X1){\unicdcdcdhd}(k1\_nat\_1~X0~np\_\_1 \in k4\_finseq\_1~X1)){\unicdbdjdcd}((r1\_xxreal\_0~np\_\_1~\\
X0){\unicdcdcdhd}(r1\_xxreal\_0~(k1\_nat\_1~X0~np\_\_1)~(k3\_finseq\_1~X1))))))\end{array}
\label{hyp:ehbdddedpfdhfgbhpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X1 .  {\unicdcdaddd} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}(\\
(v1\_funct\_1~X2){\unicdcdcdhd}(v1\_finseq\_1~X2))){\unicdcdcdhd}((k3\_finseq\_1~X2=X1){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
(v7\_ordinal1~X3){\unicdbdjdcd}((X3 \in k4\_finseq\_1~X2){\unicdbdjdcd}(k1\_funct\_1~X2~X3=X0~X3))))\end{array}
\label{hyp:dhcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}\iota{\unicdbdjdcd}o .  {\unicdcdadad} X1 .  ({\unicdcdadad} X2 .  (v7\_ordinal1~\\
X2){\unicdbdjdcd}(\preoh (X2 \in k2\_finseq\_1~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  \preoh X0~X2~X3))){\unicdbdjdcd}({\unicdcdaddd} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_finseq\_1~X2))){\unicdcdcdhd}((k4\_finseq\_1~\\
X2=k2\_finseq\_1~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}((X3 \in k2\_finseq\_1~\\
X1){\unicdbdjdcd}(X0~X3~(k1\_funct\_1~X2~X3))))))\end{array}
\label{hyp:dhbdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\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 .  (v7\_ordinal1~X1){\unicdbdjdcd}((X1 \in k4\_finseq\_1~X0){\unicdbdjdcd}((r1\_xxreal\_0~\\
X1~(k3\_finseq\_1~X0)){\unicdcdcdhd}((r1\_xxreal\_0~(k2\_nat\_1~k6\_numbers~np\_\_1)~\\
X1){\unicdcdcdhd}(\preoh r1\_xxreal\_0~X1~k6\_numbers)))))\end{array}
\label{hyp:mgcdpfchfghhchjgehfgbd}
\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~(k16\_finseq\_1~k6\_numbers~X0)){\unicdcdcdhd}((v1\_funct\_1~(k16\_finseq\_1~\\
k6\_numbers~X0)){\unicdcdcdhd}((v1\_xboole\_0~(k16\_finseq\_1~k6\_numbers~X0)){\unicdcdcdhd}\\
(v1\_finseq\_1~(k16\_finseq\_1~k6\_numbers~X0)))))\end{array}
\label{hyp:ggdgcdbdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_tarski~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X0){\unicdbdjdcd}\\
(X2 \in X1))\end{array}
\label{hyp:egddpfehbgchdhlgjg}
\end{equation}
\begin{theorem}\label{thm:mgedpfchfghhchjgehfgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}(\preoh (\preoh (\preoh r1\_xxreal\_0~X1~(k3\_finseq\_1~\\
X0)){\unicdcdcdhd}(r1\_xxreal\_0~(k3\_finseq\_1~X0)~X1)){\unicdcdcdhd}((\preoh (\preoh r1\_xxreal\_0~np\_\_1~\\
X1){\unicdcdcdhd}(r1\_xxreal\_0~X1~k6\_numbers)){\unicdcdcdhd}(\preoh X1 \in k4\_finseq\_1~X0))))\end{array}$$
\end{theorem}
\end{document}
