\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{t5\_pdiff\_8 (TMYPQQ4iDqW2bR7sb5g8ukVx2pn5WiD6QK8)}
\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 $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k17\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_pdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k12\_euclid : {{\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 $ k4\_real\_ns1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_normsp\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_pdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\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 $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_real\_ns1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_real\_ns1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_normsp\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_real\_ns1 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k4\_real\_ns1~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}(k1\_normsp\_0~\\
(k4\_real\_ns1~np\_\_1)~(k3\_funct\_2~(u1\_struct\_0~(k4\_real\_ns1~X0))~\\
(u1\_struct\_0~(k4\_real\_ns1~np\_\_1))~(k4\_pdiff\_1~X2~X0)~X1)=k17\_complex1~\\
(k1\_seq\_1~(k1\_pdiff\_1~X2~X0)~X1))))\end{array}
\label{hyp:ehedpfahegjgggggpfid}
\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~(u1\_struct\_0~(k4\_real\_ns1~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}(((r1\_xxreal\_0~\\
np\_\_1~X2){\unicdcdcdhd}(r1\_xxreal\_0~X2~X0)){\unicdbdjdcd}(r1\_xxreal\_0~(k1\_normsp\_0~(k4\_real\_ns1~\\
np\_\_1)~(k3\_funct\_2~(u1\_struct\_0~(k4\_real\_ns1~X0))~(u1\_struct\_0~\\
(k4\_real\_ns1~np\_\_1))~(k4\_pdiff\_1~X2~X0)~X1))~(k1\_normsp\_0~(k4\_real\_ns1~\\
X0)~X1)))))\end{array}
\label{hyp:ehddpfahegjgggggpfid}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
(k4\_real\_ns1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_2~X2~k1\_numbers~(k1\_euclid~\\
X0)){\unicdbdjdcd}((X1=X2){\unicdbdjdcd}(k1\_normsp\_0~(k4\_real\_ns1~X0)~X1=k12\_euclid~X2))))\end{array}
\label{hyp:ehbdpfchfgbgmgpfogdhbd}
\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 .  {\unicdcdadad} X1 .  (m1\_finseq\_2~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_2~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfcd}
\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}
{\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 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{{m1\_finseq\_2}~{({{k1\_euclid}~{X0}})}}~{k1\_numbers}})}}}\label{hyp:egehpflgbdpffgfhdgmgjgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v1\_normsp\_1~X1){\unicdcdcdhd}(l1\_normsp\_1~X1))){\unicdbdjdcd}((X1=k4\_real\_ns1~X0){\unicdbdjded}\\
((u1\_struct\_0~X1=k1\_euclid~X0){\unicdcdcdhd}((k4\_struct\_0~X1=k5\_euclid~X0){\unicdcdcdhd}\\
((r1\_funct\_2~(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~X1))~\\
(u1\_struct\_0~X1)~(k2\_zfmisc\_1~(k1\_euclid~X0)~(k1\_euclid~X0))~(\\
k1\_euclid~X0)~(u1\_algstr\_0~X1)~(k1\_real\_ns1~X0)){\unicdcdcdhd}((r1\_funct\_2~\\
(k2\_zfmisc\_1~k1\_numbers~(u1\_struct\_0~X1))~(u1\_struct\_0~X1)~(k2\_zfmisc\_1~\\
k1\_numbers~(k1\_euclid~X0))~(k1\_euclid~X0)~(u1\_rlvect\_1~X1)~(k2\_real\_ns1~\\
X0)){\unicdcdcdhd}(r1\_funct\_2~(u1\_struct\_0~X1)~k1\_numbers~(k1\_euclid~X0)~k1\_numbers~\\
(u1\_normsp\_0~X1)~(k3\_real\_ns1~X0))))))))\end{array}
\label{hyp:egedpfchfgbgmgpfogdhbd}
\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:ehfdpfahegjgggggpfid}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m2\_subset\_1~X0~k1\_numbers~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m2\_finseq\_2~X1~k1\_numbers~(k1\_euclid~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m2\_subset\_1~X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}(((r1\_xxreal\_0~np\_\_1~\\
X2){\unicdcdcdhd}(r1\_xxreal\_0~X2~X0)){\unicdbdjdcd}(r1\_xxreal\_0~(k17\_complex1~(k1\_seq\_1~\\
(k1\_pdiff\_1~X2~X0)~X1))~(k12\_euclid~X1)))))\end{array}$$
\end{theorem}
\end{document}
