\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{t21\_pdiff\_9 (TMKdsDmZWbd94scqGFwvgU2wvgPqGbihaBe)}
\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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_real\_ns1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v1\_pdiff\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_pdiff\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k12\_pdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_pdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k12\_finseq\_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 $ r4\_pdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ r2\_pdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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 .  (m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~\\
X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_euclid~X0)~\\
(k1\_euclid~X1))))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(k1\_euclid~X0))){\unicdbdjdcd}(((v1\_pdiff\_7~X4~X0){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~X2){\unicdcdcdhd}\\
(r1\_xxreal\_0~X2~X0))){\unicdbdjdcd}((r2\_pdiff\_7~X0~X1~X2~X3~X4){\unicdbdjded}((r1\_tarski~\\
X4~(k1\_relset\_1~(k1\_euclid~X0)~X3)){\unicdcdcdhd}({\unicdcdadad} X5 .  (m2\_finseq\_2~\\
X5~k1\_numbers~(k1\_euclid~X0)){\unicdbdjdcd}((X5 \in X4){\unicdbdjdcd}(r4\_pdiff\_1~X0~X1~X2~X3~\\
X5))))))))))\end{array}
\label{hyp:ehddedpfahegjgggggpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m2\_subset\_1~X1~k1\_numbers~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m2\_subset\_1~X2~k1\_numbers~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k4\_real\_ns1~X1))~(u1\_struct\_0~(k4\_real\_ns1~X2)))))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k1\_euclid~X1)~(k1\_euclid~X2))))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~\\
(u1\_struct\_0~(k4\_real\_ns1~X1))){\unicdbdjdcd}({\unicdcdadad} X6 .  (m2\_finseq\_2~X6~\\
k1\_numbers~(k1\_euclid~X1)){\unicdbdjdcd}(((X3=X4){\unicdcdcdhd}((X5=X6){\unicdcdcdhd}(r2\_pdiff\_1~\\
X2~X1~X0~X3~X5))){\unicdbdjdcd}(k1\_funct\_1~(k9\_pdiff\_1~X1~X2~X0~X3~X5)~(k12\_finseq\_1~\\
k5\_numbers~np\_\_1)=k12\_pdiff\_1~X1~X2~X0~X4~X6))))))))\end{array}
\label{hyp:ehbdhdpfahegjgggggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m2\_subset\_1~X1~k1\_numbers~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m2\_subset\_1~X2~k1\_numbers~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k4\_real\_ns1~X1))~(u1\_struct\_0~(k4\_real\_ns1~X2)))))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k1\_euclid~X1)~(k1\_euclid~X2))))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~\\
(u1\_struct\_0~(k4\_real\_ns1~X1))){\unicdbdjdcd}({\unicdcdadad} X6 .  (m2\_finseq\_2~X6~\\
k1\_numbers~(k1\_euclid~X1)){\unicdbdjdcd}(((X3=X4){\unicdcdcdhd}(X5=X6)){\unicdbdjdcd}((r2\_pdiff\_1~\\
X2~X1~X0~X3~X5){\unicdbdjded}(r4\_pdiff\_1~X1~X2~X0~X4~X6)))))))))\end{array}
\label{hyp:ehbdgdpfahegjgggggpfbd}
\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}
\begin{array}{c}{\unicdcdaddd} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
k5\_numbers))){\unicdcdcdhd}((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~\\
X0~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}\\
((v1\_partfun1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k5\_numbers){\unicdcdcdhd}\\
((v1\_valued\_0~X0){\unicdcdcdhd}((v2\_valued\_0~X0){\unicdcdcdhd}((v3\_valued\_0~X0){\unicdcdcdhd}((v4\_valued\_0~\\
X0){\unicdcdcdhd}(v5\_valued\_0~X0))))))))))))\end{array}
\label{hyp:chdgddpfghbgmgfhfgegpfad}
\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 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v1\_xboole\_0~X2))\end{array}
\label{hyp:dgdgddpfchfgmgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdbdpfahegjgggggpfjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m2\_subset\_1~X0~k1\_numbers~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m2\_subset\_1~X1~k1\_numbers~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_funct\_1~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(\\
k1\_euclid~X0)~(k1\_euclid~X1))))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}\\
(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~(k4\_real\_ns1~\\
X0))~(u1\_struct\_0~(k4\_real\_ns1~X1)))))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k1\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~\\
(k1\_zfmisc\_1~(u1\_struct\_0~(k4\_real\_ns1~X0)))){\unicdbdjdcd}(((r1\_xxreal\_0~\\
np\_\_1~X2){\unicdcdcdhd}((r1\_xxreal\_0~X2~X0){\unicdcdcdhd}((v1\_pdiff\_7~X5~X0){\unicdcdcdhd}((X4=X3){\unicdcdcdhd}\\
((X5=X6){\unicdcdcdhd}(r2\_pdiff\_7~X0~X1~X2~X3~X5)))))){\unicdbdjdcd}({\unicdcdadad} X7 .  (m2\_finseq\_2~\\
X7~k1\_numbers~(k1\_euclid~X0)){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~(u1\_struct\_0~\\
(k4\_real\_ns1~X0))){\unicdbdjdcd}(((X7 \in X5){\unicdcdcdhd}(X7=X8)){\unicdbdjdcd}(k12\_pdiff\_1~X0~X1~X2~\\
X3~X7=k1\_funct\_1~(k9\_pdiff\_1~X0~X1~X2~X4~X8)~(k12\_finseq\_1~k5\_numbers~\\
np\_\_1))))))))))))\end{array}$$
\end{theorem}
\end{document}
