\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{t31\_ndiff\_5 (TMGf9bQf2QfDHxKRQwxGzeu7taNEYh5NCnR)}
\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 $ v1\_ndiff\_5 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k14\_prvect\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_normsp\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_prvect\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_ndiff\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_prvect\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ v1\_prvect\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_ndiff\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v2\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ 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}({\unicdcdadad} X1 .  (m2\_subset\_1~\\
X1~k5\_numbers~(k4\_finseq\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(\\
u1\_struct\_0~(k14\_prvect\_2~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(k4\_card\_3~(k4\_prvect\_2~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
(k11\_prvect\_2~X0~X1))){\unicdbdjdcd}(((X3=X2){\unicdcdcdhd}(X4=k1\_funct\_1~X3~X1)){\unicdbdjdcd}(r1\_xxreal\_0~\\
(k1\_normsp\_0~(k11\_prvect\_2~X0~X1)~X4)~(k1\_normsp\_0~(k14\_prvect\_2~\\
X0)~X2)))))))\end{array}
\label{hyp:ehbdadpfahchghfgdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\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}
\label{hyp:ehbdadpfogegjgggggpffd}
\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}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))){\unicdbdjdcd}\\
(k4\_finseq\_1~X0=k9\_xtuple\_0~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))))){\unicdcdcdhd}(m1\_subset\_1~X3~X0))){\unicdbdjdcd}(k3\_funct\_2~X0~\\
X1~X2~X3=k1\_funct\_1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_relat\_1~\\
X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_finseq\_1~X0){\unicdcdcdhd}(v1\_prvect\_2~X0))))){\unicdcdcdhd}\\
((m1\_subset\_1~X1~(k4\_card\_3~(k4\_prvect\_2~X0))){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k4\_finseq\_1~X0)))){\unicdbdjdcd}(k1\_ndiff\_5~X0~X1~X2=k1\_funct\_1~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfogegjgggggpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_relat\_1~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(k9\_xtuple\_0~X0))\end{array}
\label{hyp:ggdgidpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v2\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0))){\unicdbdjdcd}\\
(\preoh v1\_xboole\_0~(k4\_card\_3~X0))\end{array}
\label{hyp:ggdgfdpfdgbgchegpfdd}
\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 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))){\unicdbdjdcd}\\
(m1\_subset\_1~(k4\_finseq\_1~X0)~(k1\_zfmisc\_1~k5\_numbers))\end{array}
\label{hyp:egehpflgedpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\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))))){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k4\_finseq\_1~X0))){\unicdbdjdcd}((v1\_funct\_1~(k3\_ndiff\_5~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~\\
(k3\_ndiff\_5~X0~X1)~(u1\_struct\_0~(k14\_prvect\_2~X0))~(u1\_struct\_0~\\
(k11\_prvect\_2~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~(k3\_ndiff\_5~X0~X1)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~(k14\_prvect\_2~X0))~(u1\_struct\_0~(k11\_prvect\_2~\\
X0~X1)))))))\end{array}
\label{hyp:egehpflgddpfogegjgggggpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))))){\unicdcdcdhd}(m1\_subset\_1~X3~X0))){\unicdbdjdcd}(m1\_subset\_1~(\\
k3\_funct\_2~X0~X1~X2~X3)~X1)\end{array}
\label{hyp:egehpflgddpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\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}({\unicdcdadad} X1 .  (m2\_subset\_1~\\
X1~k5\_numbers~(k4\_finseq\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}\\
((v1\_funct\_2~X2~(u1\_struct\_0~(k14\_prvect\_2~X0))~(u1\_struct\_0~\\
(k11\_prvect\_2~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k14\_prvect\_2~X0))~(u1\_struct\_0~(k11\_prvect\_2~X0~\\
X1))))))){\unicdbdjdcd}((X2=k3\_ndiff\_5~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(k4\_card\_3~(k4\_prvect\_2~X0))){\unicdbdjdcd}(k1\_funct\_1~X2~X3=k1\_ndiff\_5~X0~\\
X3~X1)))))\end{array}
\label{hyp:egddpfogegjgggggpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v4\_relat\_1~\\
X1~X0)){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}(v4\_relat\_1~X1~X0))))\end{array}
\label{hyp:dgdghdpfchfgmgbgehpfbd}
\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))){\unicdbdjdcd}\\
((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}\\
(v1\_finseq\_1~X0))))\end{array}
\label{hyp:dgdgfdpfggjgogdhfgbhpfbd}
\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}
\begin{theorem}\label{thm:ehddbdpfogegjgggggpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finseq\_1~X0){\unicdcdcdhd}((v2\_prvect\_2~X0){\unicdcdcdhd}(v1\_ndiff\_5~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m2\_subset\_1~X1~k5\_numbers~(k4\_finseq\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~(k14\_prvect\_2~X0))){\unicdbdjdcd}(r1\_xxreal\_0~\\
(k1\_normsp\_0~(k11\_prvect\_2~X0~X1)~(k3\_funct\_2~(u1\_struct\_0~(k14\_prvect\_2~\\
X0))~(u1\_struct\_0~(k11\_prvect\_2~X0~X1))~(k3\_ndiff\_5~X0~X1)~X2))~\\
(k1\_normsp\_0~(k14\_prvect\_2~X0)~X2))))\end{array}$$
\end{theorem}
\end{document}
