\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{t55\_vfunct\_2 (TMWrb818XW26xVvqwKn9Y4Ca1ZZLHT6YEAh)}
\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 $ v3\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_clvect\_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 $ v3\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_numbers : {\iota}$ be given.
Let $ r1\_vfunct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k2\_vfunct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k5\_vfunct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_comseq\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k3\_normsp\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v13\_algstr\_0~X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~\\
X1){\unicdcdcdhd}((v3\_normsp\_0~X1){\unicdcdcdhd}((v4\_normsp\_0~X1){\unicdcdcdhd}((v2\_clvect\_1~X1){\unicdcdcdhd}\\
((v3\_clvect\_1~X1){\unicdcdcdhd}((v4\_clvect\_1~X1){\unicdcdcdhd}((v5\_clvect\_1~X1){\unicdcdcdhd}((v8\_clvect\_1~\\
X1){\unicdcdcdhd}(l2\_clvect\_1~X1))))))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~\\
X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~(u1\_struct\_0~\\
X1))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (v3\_funct\_1~(k2\_partfun1~X0~(u1\_struct\_0~\\
X1)~X2~X3)){\unicdbdjdcd}(r1\_vfunct\_2~X0~X1~X2~X3))))\end{array}
\label{hyp:ehfdedpfghggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v13\_algstr\_0~X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~\\
X1){\unicdcdcdhd}((v3\_normsp\_0~X1){\unicdcdcdhd}((v4\_normsp\_0~X1){\unicdcdcdhd}((v2\_clvect\_1~X1){\unicdcdcdhd}\\
((v3\_clvect\_1~X1){\unicdcdcdhd}((v4\_clvect\_1~X1){\unicdcdcdhd}((v5\_clvect\_1~X1){\unicdcdcdhd}((v8\_clvect\_1~\\
X1){\unicdcdcdhd}(l2\_clvect\_1~X1))))))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~\\
X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~(u1\_struct\_0~\\
X1))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (r1\_vfunct\_2~X0~X1~X2~X3){\unicdbdjdcd}((v1\_comseq\_2~(\\
k2\_partfun1~X0~k1\_numbers~(k3\_normsp\_0~X0~X1~X2)~X3)){\unicdcdcdhd}(r1\_vfunct\_2~\\
X0~X1~(k5\_vfunct\_1~X0~X1~X2)~X3)))))\end{array}
\label{hyp:ehedfdpfghggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v13\_algstr\_0~X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~\\
X1){\unicdcdcdhd}((v3\_normsp\_0~X1){\unicdcdcdhd}((v4\_normsp\_0~X1){\unicdcdcdhd}((v2\_clvect\_1~X1){\unicdcdcdhd}\\
((v3\_clvect\_1~X1){\unicdcdcdhd}((v4\_clvect\_1~X1){\unicdcdcdhd}((v5\_clvect\_1~X1){\unicdcdcdhd}((v8\_clvect\_1~\\
X1){\unicdcdcdhd}(l2\_clvect\_1~X1))))))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~\\
X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~(u1\_struct\_0~\\
X1))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(r1\_vfunct\_2~X0~X1~X2~X4){\unicdbdjdcd}(r1\_vfunct\_2~X0~X1~(k2\_vfunct\_2~X0~X1~X2~\\
X3)~X4)))))\end{array}
\label{hyp:ehededpfghggfhogdgehpfcd}
\end{equation}
\begin{theorem}\label{thm:ehfdfdpfghggfhogdgehpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v13\_algstr\_0~X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~\\
X1){\unicdcdcdhd}((v3\_normsp\_0~X1){\unicdcdcdhd}((v4\_normsp\_0~X1){\unicdcdcdhd}((v2\_clvect\_1~X1){\unicdcdcdhd}\\
((v3\_clvect\_1~X1){\unicdcdcdhd}((v4\_clvect\_1~X1){\unicdcdcdhd}((v5\_clvect\_1~X1){\unicdcdcdhd}((v8\_clvect\_1~\\
X1){\unicdcdcdhd}(l2\_clvect\_1~X1))))))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~\\
X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~(u1\_struct\_0~\\
X1))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (v3\_funct\_1~(k2\_partfun1~X0~(u1\_struct\_0~\\
X1)~X2~X3)){\unicdbdjdcd}(({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k2\_numbers){\unicdbdjdcd}(r1\_vfunct\_2~\\
X0~X1~(k2\_vfunct\_2~X0~X1~X2~X4)~X3)){\unicdcdcdhd}((r1\_vfunct\_2~X0~X1~(k5\_vfunct\_1~\\
X0~X1~X2)~X3){\unicdcdcdhd}(v1\_comseq\_2~(k2\_partfun1~X0~k1\_numbers~(k3\_normsp\_0~\\
X0~X1~X2)~X3)))))))\end{array}$$
\end{theorem}
\end{document}
