\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\_ndiff\_4 (TMJ5VChB3tN2Vxa6hRsji44TJeqTaNJYqk7)}
\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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_real\_ns1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_ndiff\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_ndiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k7\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k1\_ndiff\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k17\_lopban\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_ndiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_normsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_normsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_normsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}\\
((v5\_rlvect\_1~X0){\unicdcdcdhd}((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_normsp\_0~X0){\unicdcdcdhd}((v4\_normsp\_0~X0){\unicdcdcdhd}((v2\_normsp\_1~X0){\unicdcdcdhd}\\
(l1\_normsp\_1~X0)))))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((\preoh v7\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((\\
v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}((v5\_rlvect\_1~X1){\unicdcdcdhd}((v6\_rlvect\_1~\\
X1){\unicdcdcdhd}((v7\_rlvect\_1~X1){\unicdcdcdhd}((v8\_rlvect\_1~X1){\unicdcdcdhd}((v3\_normsp\_0~X1){\unicdcdcdhd}\\
((v4\_normsp\_0~X1){\unicdcdcdhd}((v2\_normsp\_1~X1){\unicdcdcdhd}(l1\_normsp\_1~X1)))))))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~\\
X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~(u1\_struct\_0~\\
X0))))){\unicdbdjdcd}((r1\_ndiff\_3~X0~X3~X2){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}\\
(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1))))){\unicdbdjdcd}((r1\_ndiff\_1~X0~X1~X4~(k7\_partfun1~(u1\_struct\_0~X0)~X3~\\
X2)){\unicdbdjdcd}((r1\_ndiff\_3~X1~(k1\_partfun1~k1\_numbers~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~X3~X4)~X2){\unicdcdcdhd}(k1\_ndiff\_3~X1~(k1\_partfun1~\\
k1\_numbers~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~\\
X3~X4)~X2=k17\_lopban\_1~X0~X1~(k3\_ndiff\_1~X0~X1~X4~(k7\_partfun1~(u1\_struct\_0~\\
X0)~X3~X2))~(k1\_ndiff\_3~X0~X3~X2)))))))))\end{array}
\label{hyp:ehgdpfogegjgggggpffd}
\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}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k4\_real\_ns1~X0)){\unicdcdcdhd}\\
((v13\_algstr\_0~(k4\_real\_ns1~X0)){\unicdcdcdhd}((v2\_rlvect\_1~(k4\_real\_ns1~\\
X0)){\unicdcdcdhd}((v3\_rlvect\_1~(k4\_real\_ns1~X0)){\unicdcdcdhd}((v4\_rlvect\_1~(k4\_real\_ns1~\\
X0)){\unicdcdcdhd}((v5\_rlvect\_1~(k4\_real\_ns1~X0)){\unicdcdcdhd}((v6\_rlvect\_1~(k4\_real\_ns1~\\
X0)){\unicdcdcdhd}((v7\_rlvect\_1~(k4\_real\_ns1~X0)){\unicdcdcdhd}((v8\_rlvect\_1~(k4\_real\_ns1~\\
X0)){\unicdcdcdhd}((v3\_normsp\_0~(k4\_real\_ns1~X0)){\unicdcdcdhd}((v4\_normsp\_0~(k4\_real\_ns1~\\
X0)){\unicdcdcdhd}((v1\_normsp\_1~(k4\_real\_ns1~X0)){\unicdcdcdhd}(v2\_normsp\_1~(k4\_real\_ns1~\\
X0))))))))))))))\end{array}
\label{hyp:ggdgddpfchfgbgmgpfogdhbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v7\_ordinal1~X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k4\_real\_ns1~X0)){\unicdcdcdhd}((\preoh v7\_struct\_0~(k4\_real\_ns1~X0)){\unicdcdcdhd}(v1\_normsp\_1~\\
(k4\_real\_ns1~X0))))\end{array}
\label{hyp:ggdgcdpfchfgbgmgpfogdhbd}
\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 .  (v7\_ordinal1~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k4\_real\_ns1~X0)){\unicdcdcdhd}\\
((v1\_normsp\_1~(k4\_real\_ns1~X0)){\unicdcdcdhd}(l1\_normsp\_1~(k4\_real\_ns1~X0))))\end{array}
\label{hyp:egehpflgedpfchfgbgmgpfogdhbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehfdadpfogegjgggggpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m2\_subset\_1~X0~k1\_numbers~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m2\_subset\_1~X1~k1\_numbers~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~\\
X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~(u1\_struct\_0~\\
(k4\_real\_ns1~X0)))))){\unicdbdjdcd}((r1\_ndiff\_3~(k4\_real\_ns1~X0)~X3~X2){\unicdbdjdcd}(\\
{\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k4\_real\_ns1~X0))~(u1\_struct\_0~(k4\_real\_ns1~X1)))))){\unicdbdjdcd}\\
((r1\_ndiff\_1~(k4\_real\_ns1~X0)~(k4\_real\_ns1~X1)~X4~(k7\_partfun1~\\
(u1\_struct\_0~(k4\_real\_ns1~X0))~X3~X2)){\unicdbdjdcd}((r1\_ndiff\_3~(k4\_real\_ns1~\\
X1)~(k1\_partfun1~k1\_numbers~(u1\_struct\_0~(k4\_real\_ns1~X0))~(u1\_struct\_0~\\
(k4\_real\_ns1~X0))~(u1\_struct\_0~(k4\_real\_ns1~X1))~X3~X4)~X2){\unicdcdcdhd}(k1\_ndiff\_3~\\
(k4\_real\_ns1~X1)~(k1\_partfun1~k1\_numbers~(u1\_struct\_0~(k4\_real\_ns1~\\
X0))~(u1\_struct\_0~(k4\_real\_ns1~X0))~(u1\_struct\_0~(k4\_real\_ns1~\\
X1))~X3~X4)~X2=k17\_lopban\_1~(k4\_real\_ns1~X0)~(k4\_real\_ns1~X1)~(\\
k3\_ndiff\_1~(k4\_real\_ns1~X0)~(k4\_real\_ns1~X1)~X4~(k7\_partfun1~(\\
u1\_struct\_0~(k4\_real\_ns1~X0))~X3~X2))~(k1\_ndiff\_3~(k4\_real\_ns1~\\
X0)~X3~X2)))))))))\end{array}$$
\end{theorem}
\end{document}
