\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{t10\_ndiff\_5 (TMPxfxcynkV46ootNsZ1LW5CCCyjs2kiyuV)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_prvect\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k14\_prvect\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_prvect\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ g1\_normsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k8\_prvect\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k13\_prvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_prvect\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_prvect\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k9\_prvect\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k13\_prvect\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_prvect\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_prvect\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_prvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_normsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_normsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_normsp\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((v1\_finseq\_1~X0){\unicdcdcdhd}(v2\_prvect\_2~X0))))){\unicdbdjdcd}(k14\_prvect\_2~X0=\\
g1\_normsp\_1~(k4\_card\_3~(k4\_prvect\_2~X0))~(k8\_prvect\_2~X0)~(k13\_prvect\_1~\\
(k4\_prvect\_2~X0)~(k6\_prvect\_2~X0))~(k2\_prvect\_2~(k4\_prvect\_2~\\
X0)~k1\_numbers~(k9\_prvect\_2~X0))~(k13\_prvect\_2~X0))\end{array}
\label{hyp:ehgdpfahchghfgdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((m1\_subset\_1~\\
X1~X0){\unicdcdcdhd}(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~\\
X0))))){\unicdcdcdhd}(((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k2\_zfmisc\_1~k1\_numbers~\\
X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~X0)~X0))))){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~X0~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k1\_numbers)))))))){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  {\unicdcdadad} X6 .  {\unicdcdadad} X7 .  {\unicdcdadad} X8 .  {\unicdcdadad} X9 .  (g1\_normsp\_1~\\
X0~X1~X2~X3~X4=g1\_normsp\_1~X5~X6~X7~X8~X9){\unicdbdjdcd}((X0=X5){\unicdcdcdhd}((X1=X6){\unicdcdcdhd}((X2=\\
X7){\unicdcdcdhd}((X3=X8){\unicdcdcdhd}(X4=X9))))))\end{array}
\label{hyp:ggchfgfgpfhgbdpfogpgchngdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_numbers}}}}\label{hyp:ggdgbdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((v1\_finseq\_1~X0){\unicdcdcdhd}(v1\_prvect\_2~X0))))){\unicdbdjdcd}(m1\_prvect\_2~(k9\_prvect\_2~\\
X0)~(k4\_prvect\_2~X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgjdpfahchghfgdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((v1\_finseq\_1~X0){\unicdcdcdhd}(v1\_prvect\_2~X0))))){\unicdbdjdcd}(m1\_subset\_1~(k8\_prvect\_2~\\
X0)~(k4\_card\_3~(k4\_prvect\_2~X0)))\end{array}
\label{hyp:egehpflgidpfahchghfgdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((v1\_finseq\_1~X0){\unicdcdcdhd}(v1\_prvect\_2~X0))))){\unicdbdjdcd}(m1\_prvect\_1~(k6\_prvect\_2~\\
X0)~(k4\_prvect\_2~X0))\end{array}
\label{hyp:egehpflggdpfahchghfgdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((v1\_finseq\_1~X0){\unicdcdcdhd}(v1\_prvect\_2~X0))))){\unicdbdjdcd}((v1\_relat\_1~(k4\_prvect\_2~\\
X0)){\unicdcdcdhd}((v2\_relat\_1~(k4\_prvect\_2~X0)){\unicdcdcdhd}((v1\_funct\_1~(k4\_prvect\_2~\\
X0)){\unicdcdcdhd}((\preoh v1\_xboole\_0~(k4\_prvect\_2~X0)){\unicdcdcdhd}(v1\_finseq\_1~(k4\_prvect\_2~\\
X0))))))\end{array}
\label{hyp:egehpflgedpfahchghfgdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v2\_relat\_1~\\
X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))))){\unicdcdcdhd}\\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_prvect\_2~X2~X0~X1))){\unicdbdjdcd}((v1\_funct\_1~(k2\_prvect\_2~\\
X0~X1~X2)){\unicdcdcdhd}((v1\_funct\_2~(k2\_prvect\_2~X0~X1~X2)~(k2\_zfmisc\_1~X1~(\\
k4\_card\_3~X0))~(k4\_card\_3~X0)){\unicdcdcdhd}(m1\_subset\_1~(k2\_prvect\_2~X0~X1~\\
X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X1~(k4\_card\_3~X0))~\\
(k4\_card\_3~X0))))))\end{array}
\label{hyp:egehpflgcdpfahchghfgdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((v1\_finseq\_1~X0){\unicdcdcdhd}(v2\_prvect\_2~X0))))){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k14\_prvect\_2~X0)){\unicdcdcdhd}((v1\_normsp\_1~(k14\_prvect\_2~X0)){\unicdcdcdhd}(l1\_normsp\_1~\\
(k14\_prvect\_2~X0))))\end{array}
\label{hyp:egehpflgbdedpfahchghfgdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((v1\_finseq\_1~X0){\unicdcdcdhd}(v2\_prvect\_2~X0))))){\unicdbdjdcd}((v1\_funct\_1~(k13\_prvect\_2~\\
X0)){\unicdcdcdhd}((v1\_funct\_2~(k13\_prvect\_2~X0)~(k4\_card\_3~(k4\_prvect\_2~\\
X0))~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~(k13\_prvect\_2~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k4\_card\_3~(k4\_prvect\_2~X0))~k1\_numbers)))))\end{array}
\label{hyp:egehpflgbdddpfahchghfgdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v2\_relat\_1~X0){\unicdcdcdhd}((\\
v1\_funct\_1~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))))){\unicdcdcdhd}(m1\_prvect\_1~\\
X1~X0)){\unicdbdjdcd}((v1\_funct\_1~(k13\_prvect\_1~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k13\_prvect\_1~\\
X0~X1)~(k2\_zfmisc\_1~(k4\_card\_3~X0)~(k4\_card\_3~X0))~(k4\_card\_3~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~(k13\_prvect\_1~X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(\\
k2\_zfmisc\_1~(k4\_card\_3~X0)~(k4\_card\_3~X0))~(k4\_card\_3~X0))))))\end{array}
\label{hyp:egehpflgbdddpfahchghfgdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_finseq\_1~\\
X0){\unicdcdcdhd}(v2\_prvect\_2~X0)))){\unicdbdjdcd}((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}\\
((v1\_finseq\_1~X0){\unicdcdcdhd}(v1\_prvect\_2~X0))))\end{array}
\label{hyp:dgdgcdpfahchghfgdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_normsp\_1~X0){\unicdbdjdcd}((v1\_normsp\_1~X0){\unicdbdjdcd}(X0=g1\_normsp\_1~\\
(u1\_struct\_0~X0)~(u2\_struct\_0~X0)~(u1\_algstr\_0~X0)~(u1\_rlvect\_1~\\
X0)~(u1\_normsp\_0~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfogpgchngdhahpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdadpfogegjgggggpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finseq\_1~X0){\unicdcdcdhd}(v2\_prvect\_2~X0))))){\unicdbdjdcd}(u1\_struct\_0~(k14\_prvect\_2~\\
X0)=k4\_card\_3~(k4\_prvect\_2~X0))\end{array}$$
\end{theorem}
\end{document}
