\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\_pdiff\_5 (TMXEPypNmgvSWuZZL9WqHrmCHVwZdnzB9rX)}
\maketitle
Let $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k1\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r2\_pdiff\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_pdiff\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_pdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k1\_pdiff\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k11\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_pdiff\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_real\_1 : {{\iota}{\unicdbdjdcd}{{\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.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m2\_finseq\_2~X3~k1\_numbers~(k1\_euclid~np\_\_3)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((\\
v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_euclid~\\
np\_\_3)~k1\_numbers)))){\unicdbdjdcd}((X3=k11\_finseq\_1~X0~X1~X2){\unicdbdjdcd}(k11\_pdiff\_1~\\
np\_\_3~np\_\_2~X4~X3=k1\_fdiff\_1~(k1\_pdiff\_2~np\_\_3~np\_\_2~X4~X3)~X1))))))\end{array}
\label{hyp:ehcdadpfahegjgggggpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m2\_finseq\_2~X3~k1\_numbers~(k1\_euclid~np\_\_3)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((\\
v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_euclid~\\
np\_\_3)~k1\_numbers)))){\unicdbdjdcd}(((X3=k11\_finseq\_1~X0~X1~X2){\unicdcdcdhd}(r2\_pdiff\_5~\\
X4~X3)){\unicdbdjdcd}(k2\_pdiff\_5~X4~X3=k1\_fdiff\_1~(k1\_pdiff\_2~np\_\_3~np\_\_2~(\\
k1\_pdiff\_3~np\_\_1~np\_\_3~X4)~X3)~X1))))))\end{array}
\label{hyp:ehbdbdpfahegjgggggpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_3){\unicdcdcdhd}(m2\_subset\_1~np\_\_3~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_3~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_3~k1\_numbers))\end{array}
\label{hyp:dhahdgddpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{np\_\_3}}}}\label{hyp:dhahdgddpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X0~k5\_numbers){\unicdcdcdhd}\\
(((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_subset\_1~X1~k5\_numbers)){\unicdcdcdhd}((v1\_funct\_1~\\
X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_euclid~X1)~\\
k1\_numbers)))))){\unicdbdjdcd}((v1\_funct\_1~(k1\_pdiff\_3~X0~X1~X2)){\unicdcdcdhd}((v1\_funct\_2~\\
(k1\_pdiff\_3~X0~X1~X2)~(k1\_euclid~X1)~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
(k1\_pdiff\_3~X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_euclid~X1)~\\
k1\_numbers)))))\end{array}
\label{hyp:egehpflgbdpfahegjgggggpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k1\_euclid~np\_\_3)~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_2~X1~\\
k1\_numbers~(k1\_euclid~np\_\_3)){\unicdbdjdcd}((r2\_pdiff\_5~X0~X1){\unicdbdjded}({\unicdcdaddd} X2 .  \\
(m1\_subset\_1~X2~k1\_numbers){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~k1\_numbers){\unicdcdcdhd}\\
({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~k1\_numbers){\unicdcdcdhd}((X1=k11\_finseq\_1~X2~\\
X3~X4){\unicdcdcdhd}({\unicdcdaddd} X5 .  (m1\_rcomp\_1~X5~X3){\unicdcdcdhd}((r1\_tarski~X5~(k1\_relset\_1~\\
k1\_numbers~(k1\_pdiff\_2~np\_\_3~np\_\_2~(k1\_pdiff\_3~np\_\_1~np\_\_3~X0)~\\
X1))){\unicdcdcdhd}({\unicdcdaddd} X6 .  ((v1\_funct\_1~X6){\unicdcdcdhd}((v3\_fdiff\_1~X6){\unicdcdcdhd}(m1\_subset\_1~\\
X6~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers))))){\unicdcdcdhd}({\unicdcdaddd} X7 .  \\
((v1\_funct\_1~X7){\unicdcdcdhd}((v2\_fdiff\_1~X7){\unicdcdcdhd}(m1\_subset\_1~X7~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k1\_numbers~k1\_numbers))))){\unicdcdcdhd}({\unicdcdadad} X8 .  (m1\_subset\_1~\\
X8~k1\_numbers){\unicdbdjdcd}((X8 \in X5){\unicdbdjdcd}(k9\_real\_1~(k1\_seq\_1~(k1\_pdiff\_2~np\_\_3~\\
np\_\_2~(k1\_pdiff\_3~np\_\_1~np\_\_3~X0)~X1)~X8)~(k1\_seq\_1~(k1\_pdiff\_2~\\
np\_\_3~np\_\_2~(k1\_pdiff\_3~np\_\_1~np\_\_3~X0)~X1)~X3)=k7\_real\_1~(k1\_seq\_1~\\
X6~(k9\_real\_1~X8~X3))~(k1\_seq\_1~X7~(k9\_real\_1~X8~X3)))))))))))))))\end{array}
\label{hyp:egcdpfahegjgggggpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k11\_finseq\_1~X0~X1~X2=k7\_finseq\_1~\\
(k7\_finseq\_1~(k9\_finseq\_1~X0)~(k9\_finseq\_1~X1))~(k9\_finseq\_1~\\
X2)\end{array}
\label{hyp:egbdadpfggjgogdhfgbhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdjdpfahegjgggggpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_2~X0~k1\_numbers~(k1\_euclid~np\_\_3)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(\\
k1\_euclid~np\_\_3)~k1\_numbers)))){\unicdbdjdcd}((r2\_pdiff\_5~X1~X0){\unicdbdjdcd}(k2\_pdiff\_5~\\
X1~X0=k11\_pdiff\_1~np\_\_3~np\_\_2~(k1\_pdiff\_3~np\_\_1~np\_\_3~X1)~X0)))\end{array}$$
\end{theorem}
\end{document}
