\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{t16\_finseq\_8 (TMKB2BifNB32Ld1vJZ3Jb9zhdLt2SEcTQiR)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ k4\_finseq\_8 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_finseq\_8 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_nat\_d : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~X0){\unicdbdjdcd}(r1\_xxreal\_0~(k3\_finseq\_1~(k4\_finseq\_8~\\
X0~X1~X2))~(k3\_finseq\_1~X1))))\end{array}
\label{hyp:ehbdadpfggjgogdhfgbhpfid}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((m1\_finseq\_1~\\
X1~X0){\unicdcdcdhd}(m1\_finseq\_1~X2~X0))){\unicdbdjdcd}(m2\_finseq\_1~(k4\_finseq\_8~X0~X1~X2)~\\
X0)\end{array}
\label{hyp:egehpflgedpfggjgogdhfgbhpfid}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_finseq\_1~X3~X0){\unicdbdjdcd}\\
((X3=k4\_finseq\_8~X0~X1~X2){\unicdbdjded}((r1\_xxreal\_0~(k3\_finseq\_1~X3)~(k3\_finseq\_1~\\
X2)){\unicdcdcdhd}((X3=k3\_finseq\_8~X0~X2~np\_\_1~(k3\_finseq\_1~X3)){\unicdcdcdhd}((X3=k3\_finseq\_8~\\
X0~X1~(k2\_nat\_1~(k7\_nat\_d~(k3\_finseq\_1~X1)~(k3\_finseq\_1~X3))~np\_\_1)~\\
(k3\_finseq\_1~X1)){\unicdcdcdhd}({\unicdcdadad} X4 .  (v7\_ordinal1~X4){\unicdbdjdcd}(((r1\_xxreal\_0~\\
X4~(k3\_finseq\_1~X2)){\unicdcdcdhd}(k3\_finseq\_8~X0~X2~np\_\_1~X4=k3\_finseq\_8~X0~\\
X1~(k2\_nat\_1~(k7\_nat\_d~(k3\_finseq\_1~X1)~X4)~np\_\_1)~(k3\_finseq\_1~\\
X1))){\unicdbdjdcd}(r1\_xxreal\_0~X4~(k3\_finseq\_1~X3)))))))))))\end{array}
\label{hyp:egcdpfggjgogdhfgbhpfid}
\end{equation}
\begin{theorem}\label{thm:ehbdgdpfggjgogdhfgbhpfid}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~X0){\unicdbdjdcd}((r1\_xxreal\_0~(k3\_finseq\_1~(\\
k4\_finseq\_8~X0~X1~X2))~(k3\_finseq\_1~X1)){\unicdcdcdhd}(r1\_xxreal\_0~(k3\_finseq\_1~\\
(k4\_finseq\_8~X0~X1~X2))~(k3\_finseq\_1~X2)))))\end{array}$$
\end{theorem}
\end{document}
