\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{t17\_integr19 (TMW2Q1QQ12kR5bCJaVBT7RmELv8RLbJtKLN)}
\maketitle
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\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_measure5 : {{\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 $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_nfcont\_4 : {{\iota}{\unicdbdjdcd}{{\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 $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k3\_normsp\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_normsp\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\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 $ v1\_normsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_normsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_normsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_rlvect\_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 $ 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 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(\preoh v1\_xboole\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~(u1\_struct\_0~(k4\_real\_ns1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X1~(k1\_euclid~X0))))){\unicdbdjdcd}((X2=X3){\unicdbdjdcd}(r2\_relset\_1~X1~k1\_numbers~(k3\_normsp\_0~\\
X1~(k4\_real\_ns1~X0)~X2)~(k1\_nfcont\_4~X0~X1~X3))))))\end{array}
\label{hyp:ehjdpfogggdgpgogehpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}((r2\_relset\_1~X0~X1~X2~X3){\unicdbdjded}(X2=X3))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfchfgmgdhfgehpfbd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}(l1\_normsp\_0~X1)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~(u1\_struct\_0~X1))))))){\unicdbdjdcd}(k3\_normsp\_0~X0~X1~X2=\\
k2\_normsp\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfogpgchngdhahpfad}
\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}
{\preoh{{{v1\_xboole\_0}~{k1\_numbers}}}}\label{hyp:ggdgbdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_normsp\_0}~{X0}})}{\unicdbdjdcd}{({{({{l1\_normsp\_0}~{X0}})}{\unicdcdcdhd}{({{l2\_struct\_0}~{X0}})}})}}}\label{hyp:egehpfmgcdpfogpgchngdhahpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_normsp\_1}~{X0}})}{\unicdbdjdcd}{({{({{l1\_rlvect\_1}~{X0}})}{\unicdcdcdhd}{({{l2\_normsp\_0}~{X0}})}})}}}\label{hyp:egehpfmgbdpfogpgchngdhahpfbd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}(l1\_normsp\_0~X1)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~(u1\_struct\_0~X1))))))){\unicdbdjdcd}((v1\_funct\_1~(k3\_normsp\_0~\\
X0~X1~X2)){\unicdcdcdhd}(m1\_subset\_1~(k3\_normsp\_0~X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~k1\_numbers))))\end{array}
\label{hyp:egehpflgddpfogpgchngdhahpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X0~k5\_numbers){\unicdcdcdhd}\\
((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~\\
(k1\_euclid~X0)))))){\unicdbdjdcd}((v1\_funct\_1~(k1\_nfcont\_4~X0~X1~X2)){\unicdcdcdhd}(m1\_subset\_1~\\
(k1\_nfcont\_4~X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~k1\_numbers))))\end{array}
\label{hyp:egehpflgbdpfogggdgpgogehpfed}
\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:ehbdhdpfjgogehfghgchbdjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v2\_measure5~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~(k1\_euclid~X0))))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~X1~(k1\_euclid~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~(k1\_euclid~X0)))))){\unicdbdjdcd}((X2=X3){\unicdbdjdcd}\\
(k1\_nfcont\_4~X0~k1\_numbers~X2=k1\_nfcont\_4~X0~X1~X3)))))\end{array}$$
\end{theorem}
\end{document}
