\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{t22\_vectsp10 (TMF7onc2cLNVAmY2sqJmqkaxm5sgB9VizT2)}
\maketitle
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\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v9\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v10\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v11\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_vectsp\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_vectsp10 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m2\_vectsp\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k3\_vectsp\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v7\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_vectsp10 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ k3\_vectsp10 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_vectsp10 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_vectsp10 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}(\\
(v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~\\
X0))))))))){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v8\_vectsp\_1~\\
X1~X0){\unicdcdcdhd}((v9\_vectsp\_1~X1~X0){\unicdcdcdhd}((v10\_vectsp\_1~X1~X0){\unicdcdcdhd}((v11\_vectsp\_1~\\
X1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}\\
(l1\_vectsp\_1~X1~X0)))))))))){\unicdcdcdhd}(m1\_vectsp\_4~X2~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m2\_vectsp\_4~X3~X0~X1~X2){\unicdbdjdcd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X1))))\end{array}
\label{hyp:egehpfngcdpfghfgdgehdhahpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}\\
((v3\_group\_1~X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~\\
X0))))))))){\unicdcdcdhd}(((\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}((v8\_vectsp\_1~X1~X0){\unicdcdcdhd}\\
((v9\_vectsp\_1~X1~X0){\unicdcdcdhd}((v10\_vectsp\_1~X1~X0){\unicdcdcdhd}((v11\_vectsp\_1~X1~\\
X0){\unicdcdcdhd}(l1\_vectsp\_1~X1~X0)))))))))){\unicdcdcdhd}(m1\_vectsp\_4~X2~X0~X1))){\unicdbdjdcd}((\\
\preoh v2\_struct\_0~(k6\_vectsp10~X0~X1~X2)){\unicdcdcdhd}((v13\_algstr\_0~(k6\_vectsp10~\\
X0~X1~X2)){\unicdcdcdhd}((v2\_rlvect\_1~(k6\_vectsp10~X0~X1~X2)){\unicdcdcdhd}((v3\_rlvect\_1~\\
(k6\_vectsp10~X0~X1~X2)){\unicdcdcdhd}((v4\_rlvect\_1~(k6\_vectsp10~X0~X1~X2)){\unicdcdcdhd}\\
((v7\_vectsp\_1~(k6\_vectsp10~X0~X1~X2)~X0){\unicdcdcdhd}((v8\_vectsp\_1~(k6\_vectsp10~\\
X0~X1~X2)~X0){\unicdcdcdhd}((v9\_vectsp\_1~(k6\_vectsp10~X0~X1~X2)~X0){\unicdcdcdhd}((v10\_vectsp\_1~\\
(k6\_vectsp10~X0~X1~X2)~X0){\unicdcdcdhd}((v11\_vectsp\_1~(k6\_vectsp10~X0~X1~X2)~\\
X0){\unicdcdcdhd}(l1\_vectsp\_1~(k6\_vectsp10~X0~X1~X2)~X0)))))))))))\end{array}
\label{hyp:egehpflggdpfghfgdgehdhahbdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}\\
((v3\_group\_1~X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~\\
X0))))))))){\unicdcdcdhd}(((\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}((v8\_vectsp\_1~X1~X0){\unicdcdcdhd}\\
((v9\_vectsp\_1~X1~X0){\unicdcdcdhd}((v10\_vectsp\_1~X1~X0){\unicdcdcdhd}((v11\_vectsp\_1~X1~\\
X0){\unicdcdcdhd}(l1\_vectsp\_1~X1~X0)))))))))){\unicdcdcdhd}(m1\_vectsp\_4~X2~X0~X1))){\unicdbdjdcd}((\\
\preoh v1\_xboole\_0~(k2\_vectsp10~X0~X1~X2)){\unicdcdcdhd}(m1\_subset\_1~(k2\_vectsp10~\\
X0~X1~X2)~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~X1)))))\end{array}
\label{hyp:egehpflgcdpfghfgdgehdhahbdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}\\
((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v8\_vectsp\_1~\\
X1~X0){\unicdcdcdhd}((v9\_vectsp\_1~X1~X0){\unicdcdcdhd}((v10\_vectsp\_1~X1~X0){\unicdcdcdhd}((v11\_vectsp\_1~\\
X1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}\\
(l1\_vectsp\_1~X1~X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_vectsp\_4~X2~X0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~X1))){\unicdbdjdcd}\\
((m2\_vectsp\_4~X3~X0~X1~X2){\unicdbdjded}({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
X1)){\unicdcdcdhd}(X3=k3\_vectsp\_4~X0~X1~X4~X2))))))\end{array}
\label{hyp:eggdpfghfgdgehdhahpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}(\\
(v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}(l6\_algstr\_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}((v8\_vectsp\_1~X1~X0){\unicdcdcdhd}\\
((v9\_vectsp\_1~X1~X0){\unicdcdcdhd}((v10\_vectsp\_1~X1~X0){\unicdcdcdhd}((v11\_vectsp\_1~X1~\\
X0){\unicdcdcdhd}(l1\_vectsp\_1~X1~X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_vectsp\_4~X2~\\
X0~X1){\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}((v7\_vectsp\_1~\\
X3~X0){\unicdcdcdhd}((v8\_vectsp\_1~X3~X0){\unicdcdcdhd}((v9\_vectsp\_1~X3~X0){\unicdcdcdhd}((v10\_vectsp\_1~\\
X3~X0){\unicdcdcdhd}((v11\_vectsp\_1~X3~X0){\unicdcdcdhd}(l1\_vectsp\_1~X3~X0))))))))))){\unicdbdjdcd}(\\
(X3=k6\_vectsp10~X0~X1~X2){\unicdbdjded}((u1\_struct\_0~X3=k2\_vectsp10~X0~X1~X2){\unicdcdcdhd}\\
((r1\_funct\_2~(k2\_zfmisc\_1~(u1\_struct\_0~X3)~(u1\_struct\_0~X3))~\\
(u1\_struct\_0~X3)~(k2\_zfmisc\_1~(k2\_vectsp10~X0~X1~X2)~(k2\_vectsp10~\\
X0~X1~X2))~(k2\_vectsp10~X0~X1~X2)~(u1\_algstr\_0~X3)~(k3\_vectsp10~X0~\\
X1~X2)){\unicdcdcdhd}((k4\_struct\_0~X3=k4\_vectsp10~X0~X1~X2){\unicdcdcdhd}(r1\_funct\_2~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X3))~(u1\_struct\_0~X3)~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(k2\_vectsp10~X0~X1~X2))~(k2\_vectsp10~X0~X1~X2)~(\\
u1\_vectsp\_1~X0~X3)~(k5\_vectsp10~X0~X1~X2)))))))))\end{array}
\label{hyp:eggdpfghfgdgehdhahbdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}(\\
(v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}(l6\_algstr\_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}((v8\_vectsp\_1~X1~X0){\unicdcdcdhd}\\
((v9\_vectsp\_1~X1~X0){\unicdcdcdhd}((v10\_vectsp\_1~X1~X0){\unicdcdcdhd}((v11\_vectsp\_1~X1~\\
X0){\unicdcdcdhd}(l1\_vectsp\_1~X1~X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_vectsp\_4~X2~\\
X0~X1){\unicdbdjdcd}(k2\_vectsp10~X0~X1~X2=ReplSep~(toset~({\uniddcgcg} X3 : \iota .  m2\_vectsp\_4~\\
X3~X0~X1~X2))~({\uniddcgcg} X3 : \iota .  True)~({\uniddcgcg} X3 : \iota .  X3))))\end{array}
\label{hyp:egcdpfghfgdgehdhahbdad}
\end{equation}
\begin{theorem}\label{thm:ehcdcdpfghfgdgehdhahbdad}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}(\\
(v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v2\_rlvect\_1~\\
X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}((v8\_vectsp\_1~X1~X0){\unicdcdcdhd}\\
((v9\_vectsp\_1~X1~X0){\unicdcdcdhd}((v10\_vectsp\_1~X1~X0){\unicdcdcdhd}((v11\_vectsp\_1~X1~\\
X0){\unicdcdcdhd}(l1\_vectsp\_1~X1~X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_vectsp\_4~X2~\\
X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(k6\_vectsp10~\\
X0~X1~X2))){\unicdbdjdcd}((m2\_vectsp\_4~X3~X0~X1~X2){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~X1)){\unicdcdcdhd}(X3=k3\_vectsp\_4~X0~X1~X4~X2))))))\end{array}$$
\end{theorem}
\end{document}
