\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{t44\_pdiff\_9 (TMNXhFkndzTtGnat4ETWGPGVNJQkPiZfSqm)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\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 $ k1\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k3\_pdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_pdiff\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r4\_pdiff\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k2\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r2\_nfcont\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r3\_pdiff\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
{\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k1\_euclid~X0)~k1\_numbers)))){\unicdbdjdcd}(r2\_relset\_1~(k1\_euclid~X0)~(k1\_euclid~\\
np\_\_1)~(k3\_pdiff\_1~X0~(k2\_partfun1~(k1\_euclid~X0)~k1\_numbers~X2~\\
X1))~(k2\_partfun1~(k1\_euclid~X0)~(k1\_euclid~np\_\_1)~(k3\_pdiff\_1~\\
X0~X2)~X1)))\end{array}
\label{hyp:ehfdpfahegjgggggpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(\\
k1\_euclid~X0)~k1\_numbers)))){\unicdbdjdcd}(k1\_relset\_1~(k1\_euclid~X0)~(k3\_pdiff\_1~\\
X0~X1)=k1\_relset\_1~(k1\_euclid~X0)~X1))\end{array}
\label{hyp:ehddpfahegjgggggpfjd}
\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 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k1\_euclid~X0)~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_2~X2~k1\_numbers~\\
(k1\_euclid~X0)){\unicdbdjdcd}((r2\_nfcont\_4~X0~X1~X2){\unicdbdjded}(r3\_pdiff\_7~X0~np\_\_1~(\\
k3\_pdiff\_1~X0~X1)~X2))))\end{array}
\label{hyp:ehddhdpfahegjgggggpfjd}
\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}
{\preoh{{{v1\_xboole\_0}~{np\_\_1}}}}\label{hyp:dhahdgbdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}((r2\_relset\_1~X0~X1~X2~X3){\unicdbdjded}(X2=X3))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_funct\_1~X2){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}(k2\_partfun1~\\
X0~X1~X2~X3=k5\_relat\_1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v4\_relat\_1~X1~X0)){\unicdbdjdcd}(\\
k1\_relset\_1~X0~X1=k9\_xtuple\_0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}((v1\_relat\_1~\\
(k5\_relat\_1~X0~X1)){\unicdcdcdhd}(v1\_funct\_1~(k5\_relat\_1~X0~X1)))\end{array}
\label{hyp:ggdgidpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_numbers}}}}\label{hyp:ggdgbdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k5\_numbers}}~{({{k1\_zfmisc\_1}~{k1\_numbers}})}}\label{hyp:egehpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_euclid~X0)~k1\_numbers))))){\unicdbdjdcd}\\
((v1\_funct\_1~(k3\_pdiff\_1~X0~X1)){\unicdcdcdhd}(m1\_subset\_1~(k3\_pdiff\_1~X0~\\
X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_euclid~X0)~(k1\_euclid~np\_\_1)))))\end{array}
\label{hyp:egehpflgddpfahegjgggggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_funct\_1~X2){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}((v1\_funct\_1~\\
(k2\_partfun1~X0~X1~X2~X3)){\unicdcdcdhd}(m1\_subset\_1~(k2\_partfun1~X0~X1~X2~X3)~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))))\end{array}
\label{hyp:egehpflgcdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X0~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_subset\_1~X1~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k1\_euclid~X0)~(k1\_euclid~X1))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (r4\_pdiff\_7~X0~\\
X1~X2~X3){\unicdbdjded}((r1\_tarski~X3~(k1\_relset\_1~(k1\_euclid~X0)~X2)){\unicdcdcdhd}({\unicdcdadad} X4 .  \\
(m2\_finseq\_2~X4~k1\_numbers~(k1\_euclid~X0)){\unicdbdjdcd}((X4 \in X3){\unicdbdjdcd}(r3\_pdiff\_7~\\
X0~X1~(k2\_partfun1~(k1\_euclid~X0)~(k1\_euclid~X1)~X2~X3)~X4)))))))\end{array}
\label{hyp:eghdpfahegjgggggpfhd}
\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 .  {\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k1\_euclid~X0)~k1\_numbers)))){\unicdbdjdcd}((r1\_pdiff\_9~X0~X1~\\
X2){\unicdbdjded}({\unicdcdadad} X3 .  (m2\_finseq\_2~X3~k1\_numbers~(k1\_euclid~X0)){\unicdbdjdcd}(\\
(X3 \in X1){\unicdbdjdcd}(r2\_nfcont\_4~X0~(k2\_partfun1~(k1\_euclid~X0)~k1\_numbers~\\
X2~X1)~X3)))))\end{array}
\label{hyp:egcdpfahegjgggggpfjd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}(v5\_relat\_1~X2~X1))\end{array}
\label{hyp:dgdgcdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v1\_relat\_1~X2)\end{array}
\label{hyp:dgdgbdpfchfgmgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehededpfahegjgggggpfjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m2\_subset\_1~X0~k1\_numbers~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k1\_euclid~X0)~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~\\
X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_euclid~X0)~\\
(k1\_euclid~np\_\_1))))){\unicdbdjdcd}((r2\_relset\_1~(k1\_euclid~X0)~(k1\_euclid~\\
np\_\_1)~(k3\_pdiff\_1~X0~X2)~X3){\unicdbdjdcd}(((r1\_tarski~X1~(k1\_relset\_1~(k1\_euclid~\\
X0)~X2)){\unicdcdcdhd}(r1\_pdiff\_9~X0~X1~X2)){\unicdbdjded}(r4\_pdiff\_7~X0~np\_\_1~X3~X1)))))\end{array}$$
\end{theorem}
\end{document}
