\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{t50\_pdiff\_5 (TMFee5mgbqwDwGZWr7ThTxywUHHApYf3953)}
\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 $ r5\_pdiff\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r3\_pdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k3\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k1\_pdiff\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k11\_pdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k7\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_pdiff\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_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 $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Assume the following.
\begin{equation}
\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}((r5\_pdiff\_5~X1~X0){\unicdbdjdcd}(k5\_pdiff\_5~\\
X1~X0=k11\_pdiff\_1~np\_\_3~np\_\_2~(k1\_pdiff\_3~np\_\_2~np\_\_3~X1)~X0)))\end{array}
\label{hyp:ehddcdpfahegjgggggpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m2\_subset\_1~X0~k1\_numbers~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(\\
k1\_euclid~X0)~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}(\\
m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_euclid~X0)~k1\_numbers)))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m2\_finseq\_2~X4~k1\_numbers~(k1\_euclid~X0)){\unicdbdjdcd}(((r3\_pdiff\_1~\\
X0~X1~X2~X4){\unicdcdcdhd}(r3\_pdiff\_1~X0~X1~X3~X4)){\unicdbdjdcd}((r3\_pdiff\_1~X0~X1~(k3\_valued\_1~\\
(k1\_euclid~X0)~k1\_numbers~k1\_numbers~X2~X3)~X4){\unicdcdcdhd}(k11\_pdiff\_1~X0~\\
X1~(k3\_valued\_1~(k1\_euclid~X0)~k1\_numbers~k1\_numbers~X2~X3)~X4=\\
k7\_real\_1~(k11\_pdiff\_1~X0~X1~X2~X4)~(k11\_pdiff\_1~X0~X1~X3~X4))))))))\end{array}
\label{hyp:ehcdjdpfahegjgggggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\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}((r5\_pdiff\_5~X1~X0){\unicdbdjded}(r3\_pdiff\_1~\\
np\_\_3~np\_\_2~(k1\_pdiff\_3~np\_\_2~np\_\_3~X1)~X0)))\end{array}
\label{hyp:ehcdddpfahegjgggggpffd}
\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\_\_2){\unicdcdcdhd}(m2\_subset\_1~np\_\_2~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_2~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_2~k1\_numbers))\end{array}
\label{hyp:dhahdgcdpfogfhngfgchbgmgdh}
\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}
\begin{theorem}\label{thm:ehfdadpfahegjgggggpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_2~X0~k1\_numbers~(k1\_euclid~np\_\_3)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(\\
k1\_euclid~np\_\_3)~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_euclid~np\_\_3)~k1\_numbers)))){\unicdbdjdcd}\\
(((r5\_pdiff\_5~X1~X0){\unicdcdcdhd}(r5\_pdiff\_5~X2~X0)){\unicdbdjdcd}((r3\_pdiff\_1~np\_\_3~np\_\_2~\\
(k3\_valued\_1~(k1\_euclid~np\_\_3)~k1\_numbers~k1\_numbers~(k1\_pdiff\_3~\\
np\_\_2~np\_\_3~X1)~(k1\_pdiff\_3~np\_\_2~np\_\_3~X2))~X0){\unicdcdcdhd}(k11\_pdiff\_1~np\_\_3~\\
np\_\_2~(k3\_valued\_1~(k1\_euclid~np\_\_3)~k1\_numbers~k1\_numbers~(k1\_pdiff\_3~\\
np\_\_2~np\_\_3~X1)~(k1\_pdiff\_3~np\_\_2~np\_\_3~X2))~X0=k7\_real\_1~(k5\_pdiff\_5~\\
X1~X0)~(k5\_pdiff\_5~X2~X0))))))\end{array}$$
\end{theorem}
\end{document}
