\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{t24\_pdiff\_9 (TMQ4wp2AoNHLGbkWDT8tMnRBozKaP3MRtMX)}
\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 $ v1\_pdiff\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ r2\_pdiff\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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\_pdiff\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ r2\_ndiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ r3\_nfcont\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k16\_lopban\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_ndiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ r7\_pdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ k15\_pdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ v3\_nfcont\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
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 .  ((\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))))){\unicdbdjdcd}((((r2\_pdiff\_7~X0~X1~X2~X3~X5){\unicdcdcdhd}(r4\_pdiff\_7~X0~X1~(k2\_pdiff\_7~\\
X0~X1~X2~X3~X5)~X5)){\unicdbdjdcd}((r7\_pdiff\_1~X0~X1~X2~X4~X6){\unicdcdcdhd}(r3\_nfcont\_1~(k4\_real\_ns1~\\
X0)~(k16\_lopban\_1~(k4\_real\_ns1~np\_\_1)~(k4\_real\_ns1~X1))~(k15\_pdiff\_1~\\
X0~X1~X2~X4~X6)~X6))){\unicdcdcdhd}(((r7\_pdiff\_1~X0~X1~X2~X4~X6){\unicdcdcdhd}(r3\_nfcont\_1~(\\
k4\_real\_ns1~X0)~(k16\_lopban\_1~(k4\_real\_ns1~np\_\_1)~(k4\_real\_ns1~\\
X1))~(k15\_pdiff\_1~X0~X1~X2~X4~X6)~X6)){\unicdbdjdcd}((r2\_pdiff\_7~X0~X1~X2~X3~X5){\unicdcdcdhd}\\
(r4\_pdiff\_7~X0~X1~(k2\_pdiff\_7~X0~X1~X2~X3~X5)~X5)))))))))))\end{array}
\label{hyp:ehcdddpfahegjgggggpfjd}
\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 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(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~\\
(u1\_struct\_0~(k4\_real\_ns1~X0))~(u1\_struct\_0~(k4\_real\_ns1~X1)))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~(k4\_real\_ns1~\\
X0)))){\unicdbdjdcd}((v3\_nfcont\_1~X3~(k4\_real\_ns1~X0)){\unicdbdjdcd}(({\unicdcdadad} X4 .  (m2\_subset\_1~\\
X4~k1\_numbers~k5\_numbers){\unicdbdjdcd}(((r1\_xxreal\_0~np\_\_1~X4){\unicdcdcdhd}(r1\_xxreal\_0~\\
X4~X0)){\unicdbdjdcd}((r7\_pdiff\_1~X0~X1~X4~X2~X3){\unicdcdcdhd}(r3\_nfcont\_1~(k4\_real\_ns1~\\
X0)~(k16\_lopban\_1~(k4\_real\_ns1~np\_\_1)~(k4\_real\_ns1~X1))~(k15\_pdiff\_1~\\
X0~X1~X4~X2~X3)~X3)))){\unicdbdjded}((r2\_ndiff\_1~X3~(k4\_real\_ns1~X0)~(k4\_real\_ns1~\\
X1)~X2){\unicdcdcdhd}(r3\_nfcont\_1~(k4\_real\_ns1~X0)~(k16\_lopban\_1~(k4\_real\_ns1~\\
X0)~(k4\_real\_ns1~X1))~(k4\_ndiff\_1~(k4\_real\_ns1~X0)~(k4\_real\_ns1~\\
X1)~X2~X3)~X3)))))))\end{array}
\label{hyp:ehcdcdpfahegjgggggpfid}
\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 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~(k4\_real\_ns1~X0)))){\unicdbdjdcd}\\
((X1=X2){\unicdbdjdcd}((v1\_pdiff\_7~X1~X0){\unicdbdjded}(v3\_nfcont\_1~X2~(k4\_real\_ns1~X0))))))\end{array}
\label{hyp:ehbdadpfahegjgggggpfjd}
\end{equation}
\begin{theorem}\label{thm:ehcdedpfahegjgggggpfjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m2\_subset\_1~X0~k1\_numbers~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m2\_subset\_1~X1~k1\_numbers~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k1\_euclid~X0)~(k1\_euclid~X1))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~(k4\_real\_ns1~\\
X0))~(u1\_struct\_0~(k4\_real\_ns1~X1)))))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(k1\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~\\
(k1\_zfmisc\_1~(u1\_struct\_0~(k4\_real\_ns1~X0)))){\unicdbdjdcd}(((X4=X5){\unicdcdcdhd}((\\
v1\_pdiff\_7~X4~X0){\unicdcdcdhd}(X2=X3))){\unicdbdjdcd}(({\unicdcdadad} X6 .  (m2\_subset\_1~X6~k1\_numbers~\\
k5\_numbers){\unicdbdjdcd}(((r1\_xxreal\_0~np\_\_1~X6){\unicdcdcdhd}(r1\_xxreal\_0~X6~X0)){\unicdbdjdcd}(\\
(r2\_pdiff\_7~X0~X1~X6~X2~X4){\unicdcdcdhd}(r4\_pdiff\_7~X0~X1~(k2\_pdiff\_7~X0~X1~X6~\\
X2~X4)~X4)))){\unicdbdjded}((r2\_ndiff\_1~X5~(k4\_real\_ns1~X0)~(k4\_real\_ns1~X1)~\\
X3){\unicdcdcdhd}(r3\_nfcont\_1~(k4\_real\_ns1~X0)~(k16\_lopban\_1~(k4\_real\_ns1~\\
X0)~(k4\_real\_ns1~X1))~(k4\_ndiff\_1~(k4\_real\_ns1~X0)~(k4\_real\_ns1~\\
X1)~X3~X5)~X5)))))))))\end{array}$$
\end{theorem}
\end{document}
