\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t56\_vfunct\_1 (TMQZcSSctNBv8eedJ7Ea8w5QKkfbiyiNquF)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_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 $ v1\_funct\_1 : {{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_vfunct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v3\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_vfunct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~\\
X2){\unicdcdcdhd}((v13\_algstr\_0~X2){\unicdcdcdhd}((v2\_rlvect\_1~X2){\unicdcdcdhd}((v3\_rlvect\_1~X2){\unicdcdcdhd}\\
((v4\_rlvect\_1~X2){\unicdcdcdhd}((v5\_rlvect\_1~X2){\unicdcdcdhd}((v6\_rlvect\_1~X2){\unicdcdcdhd}((v7\_rlvect\_1~\\
X2){\unicdcdcdhd}((v8\_rlvect\_1~X2){\unicdcdcdhd}((v3\_normsp\_0~X2){\unicdcdcdhd}((v4\_normsp\_0~X2){\unicdcdcdhd}\\
((v2\_normsp\_1~X2){\unicdcdcdhd}(l1\_normsp\_1~X2))))))))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_funct\_1~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~\\
(u1\_struct\_0~X2))))){\unicdbdjdcd}((v3\_funct\_1~(k2\_partfun1~X1~(u1\_struct\_0~\\
X2)~X3~X0)){\unicdbdjdcd}(r1\_vfunct\_1~X1~X2~X3~X0))))\end{array}
\label{hyp:ehfdedpfghggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((\preoh v2\_struct\_0~X3){\unicdcdcdhd}((v13\_algstr\_0~X3){\unicdcdcdhd}((v2\_rlvect\_1~X3){\unicdcdcdhd}((\\
v3\_rlvect\_1~X3){\unicdcdcdhd}((v4\_rlvect\_1~X3){\unicdcdcdhd}((v5\_rlvect\_1~X3){\unicdcdcdhd}((v6\_rlvect\_1~\\
X3){\unicdcdcdhd}((v7\_rlvect\_1~X3){\unicdcdcdhd}((v8\_rlvect\_1~X3){\unicdcdcdhd}((v3\_normsp\_0~X3){\unicdcdcdhd}\\
((v4\_normsp\_0~X3){\unicdcdcdhd}((v2\_normsp\_1~X3){\unicdcdcdhd}(l1\_normsp\_1~X3))))))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X2~(u1\_struct\_0~X3))))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~X5){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X2~(u1\_struct\_0~X3))))){\unicdbdjdcd}(((r1\_vfunct\_1~\\
X2~X3~X4~X0){\unicdcdcdhd}(r1\_vfunct\_1~X2~X3~X5~X1)){\unicdbdjdcd}(r1\_vfunct\_1~X2~X3~(k6\_vfunct\_1~\\
X2~X3~X4~X5)~(k3\_xboole\_0~X0~X1))))))\end{array}
\label{hyp:ehedgdpfghggfhogdgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehfdgdpfghggfhogdgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((\preoh v2\_struct\_0~X3){\unicdcdcdhd}((v13\_algstr\_0~X3){\unicdcdcdhd}((v2\_rlvect\_1~X3){\unicdcdcdhd}((\\
v3\_rlvect\_1~X3){\unicdcdcdhd}((v4\_rlvect\_1~X3){\unicdcdcdhd}((v5\_rlvect\_1~X3){\unicdcdcdhd}((v6\_rlvect\_1~\\
X3){\unicdcdcdhd}((v7\_rlvect\_1~X3){\unicdcdcdhd}((v8\_rlvect\_1~X3){\unicdcdcdhd}((v3\_normsp\_0~X3){\unicdcdcdhd}\\
((v4\_normsp\_0~X3){\unicdcdcdhd}((v2\_normsp\_1~X3){\unicdcdcdhd}(l1\_normsp\_1~X3))))))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X2~(u1\_struct\_0~X3))))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~X5){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X2~(u1\_struct\_0~X3))))){\unicdbdjdcd}(((r1\_vfunct\_1~\\
X2~X3~X4~X0){\unicdcdcdhd}(v3\_funct\_1~(k2\_partfun1~X2~(u1\_struct\_0~X3)~X5~X1))){\unicdbdjdcd}\\
(r1\_vfunct\_1~X2~X3~(k6\_vfunct\_1~X2~X3~X4~X5)~(k3\_xboole\_0~X0~X1))))))\end{array}$$
\end{theorem}
\end{document}
