\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{t29\_filerec1 (TMFoV6nZLLhfn7LgxmYCVVfDkUEXJuhY5EJ)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r5\_finseq\_8 : {{\iota}{\unicdbdjdcd}{{\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 $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k3\_finseq\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k7\_nat\_d : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ r4\_finseq\_8 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k8\_finseq\_8 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ 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}(((\preoh r1\_xxreal\_0~(k3\_finseq\_1~\\
X2)~k6\_numbers){\unicdbdjdcd}((r1\_xxreal\_0~(k3\_finseq\_1~X2)~(k3\_finseq\_1~\\
X1)){\unicdcdcdhd}(k3\_finseq\_6~X0~X1~(k7\_nat\_d~(k2\_nat\_1~(k3\_finseq\_1~X1)~np\_\_1)~\\
(k3\_finseq\_1~X2))~(k3\_finseq\_1~X1)=X2))){\unicdbdjdcd}(r4\_finseq\_8~X0~X1~X2))))\end{array}
\label{hyp:ehcdfdpfggjgogdhfgbhpfid}
\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}((r4\_finseq\_8~X0~X1~X2){\unicdbdjdcd}(r1\_xxreal\_0~\\
(k3\_finseq\_1~X2)~(k3\_finseq\_1~X1)))))\end{array}
\label{hyp:ehcdddpfggjgogdhfgbhpfid}
\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 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~X0){\unicdbdjdcd}((r5\_finseq\_8~X0~X1~X2){\unicdbdjded}((\preoh r1\_xxreal\_0~\\
(k3\_finseq\_1~X2)~k6\_numbers){\unicdbdjdcd}((r1\_xxreal\_0~(k3\_finseq\_1~X2)~\\
(k3\_finseq\_1~X1)){\unicdcdcdhd}(k8\_finseq\_8~X0~X1~X2~np\_\_1=k7\_nat\_d~(k2\_nat\_1~\\
(k3\_finseq\_1~X1)~np\_\_1)~(k3\_finseq\_1~X2)))))))\end{array}
\label{hyp:egbdcdpfggjgogdhfgbhpfid}
\end{equation}
\begin{theorem}\label{thm:ehcdjdpfggjgmgfgchfgdgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_finseq\_1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_finseq\_1~X2~X0){\unicdbdjdcd}((r5\_finseq\_8~X0~X1~X2){\unicdbdjdcd}(r1\_xxreal\_0~\\
(k3\_finseq\_1~X2)~(k3\_finseq\_1~X1)))))\end{array}$$
\end{theorem}
\end{document}
