\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{t14\_rsspace (TMLUy6eUzaHYhDLez4M1F1odKmmKVPqrXff)}
\maketitle
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_rsspace : {\iota}$ be given.
Let $ k1\_rsspace : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_rsspace : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_series\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k26\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ g1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_rsspace : {\iota}$ be given.
Let $ k4\_rsspace : {\iota}$ be given.
Let $ k5\_rsspace : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v13\_algstr\_0 : {{\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 $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ u1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~(g1\_rlvect\_1~k1\_rsspace~k6\_rsspace~k4\_rsspace~\\
k5\_rsspace))){\unicdbdjdcd}(k1\_rlvect\_1~(g1\_rlvect\_1~k1\_rsspace~k6\_rsspace~\\
k4\_rsspace~k5\_rsspace)~X1~X0=k26\_valued\_1~k5\_numbers~k1\_numbers~\\
(k2\_rsspace~X1)~X0))\end{array}
\label{hyp:ehddpfchdhdhahbgdgfg}
\end{equation}
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}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v2\_rlvect\_1~X0){\unicdcdcdhd}(l1\_algstr\_0~\\
X0)){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}(k3\_rlvect\_1~X0~X1~X2=k1\_algstr\_0~X0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfchmgghfgdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_subset\_1~X1~\\
X0){\unicdcdcdhd}(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~\\
X0))))){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k2\_zfmisc\_1~k1\_numbers~\\
X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~X0)~X0))))))){\unicdbdjdcd}({\unicdcdadad} X4 .  {\unicdcdadad} X5 .  {\unicdcdadad} X6 .  {\unicdcdadad} X7 .  \\
(g1\_rlvect\_1~X0~X1~X2~X3=g1\_rlvect\_1~X4~X5~X6~X7){\unicdbdjdcd}((X0=X4){\unicdcdcdhd}((X1=\\
X5){\unicdcdcdhd}((X2=X6){\unicdcdcdhd}(X3=X7)))))\end{array}
\label{hyp:ggchfgfgpfhgbdpfchmgghfgdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v13\_algstr\_0~k7\_rsspace){\unicdcdcdhd}((v2\_rlvect\_1~k7\_rsspace){\unicdcdcdhd}((v3\_rlvect\_1~\\
k7\_rsspace){\unicdcdcdhd}((v4\_rlvect\_1~k7\_rsspace){\unicdcdcdhd}((v5\_rlvect\_1~k7\_rsspace){\unicdcdcdhd}\\
((v6\_rlvect\_1~k7\_rsspace){\unicdcdcdhd}((v7\_rlvect\_1~k7\_rsspace){\unicdcdcdhd}(v8\_rlvect\_1~\\
k7\_rsspace)))))))\end{array}
\label{hyp:ggdgddpfchdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v2\_struct\_0}~{k7\_rsspace}}}})}{\unicdcdcdhd}{({{v1\_rlvect\_1}~{k7\_rsspace}})}}\label{hyp:ggdgcdpfchdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l2\_struct\_0}~{X0}})}{\unicdcdcdhd}{({{l1\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmgcdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_rlvect\_1}~{X0}})}{\unicdbdjdcd}{({{l2\_algstr\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfchmgghfgdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{l1\_rlvect\_1}~{k7\_rsspace}}\label{hyp:egehpflghdpfchdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k6\_rsspace}}~{k1\_rsspace}}\label{hyp:egehpflggdpfchdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k5\_rsspace){\unicdcdcdhd}((v1\_funct\_2~k5\_rsspace~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_rsspace)~k1\_rsspace){\unicdcdcdhd}(m1\_subset\_1~k5\_rsspace~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_rsspace)~\\
k1\_rsspace))))\end{array}
\label{hyp:egehpflgfdpfchdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k4\_rsspace){\unicdcdcdhd}((v1\_funct\_2~k4\_rsspace~(k2\_zfmisc\_1~\\
k1\_rsspace~k1\_rsspace)~k1\_rsspace){\unicdcdcdhd}(m1\_subset\_1~k4\_rsspace~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~k1\_rsspace~k1\_rsspace)~\\
k1\_rsspace))))\end{array}
\label{hyp:egehpflgedpfchdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_funct\_1~(k2\_rsspace~X0)){\unicdcdcdhd}((v1\_funct\_2~(k2\_rsspace~\\
X0)~k5\_numbers~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~(k2\_rsspace~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))\end{array}
\label{hyp:egehpflgcdpfchdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_rsspace}}}}\label{hyp:egehpflgbdpfchdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
{{k7\_rsspace}={{{{{g1\_rlvect\_1}~{k1\_rsspace}}~{k6\_rsspace}}~{k4\_rsspace}}~{k5\_rsspace}}}\label{hyp:eghdpfchdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~(k2\_zfmisc\_1~k1\_rsspace~\\
k1\_rsspace)~k1\_rsspace){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~k1\_rsspace~k1\_rsspace)~k1\_rsspace))))){\unicdbdjdcd}((X0=k4\_rsspace){\unicdbdjded}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k1\_rsspace){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~k1\_rsspace){\unicdbdjdcd}(k5\_binop\_1~k1\_rsspace~X0~X1~X2=k1\_series\_1~k1\_numbers~\\
(k2\_rsspace~X1)~(k2\_rsspace~X2)))))\end{array}
\label{hyp:egedpfchdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{X0} \in {k1\_rsspace}})}{\unicdbdjdcd}{({{{k2\_rsspace}~{X0}}={X0}})}}}\label{hyp:egcdpfchdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((X0=k1\_rsspace){\unicdbdjded}({\unicdcdadad} X1 .  \\
(X1 \in X0){\unicdbdjded}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers)))))))\end{array}
\label{hyp:egbdpfchdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_algstr\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}(k1\_algstr\_0~\\
X0~X1~X2=k5\_binop\_1~(u1\_struct\_0~X0)~(u1\_algstr\_0~X0)~X1~X2)))\end{array}
\label{hyp:egbdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_rlvect\_1~X0){\unicdbdjdcd}((v1\_rlvect\_1~X0){\unicdbdjdcd}(X0=g1\_rlvect\_1~\\
(u1\_struct\_0~X0)~(u2\_struct\_0~X0)~(u1\_algstr\_0~X0)~(u1\_rlvect\_1~\\
X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfchmgghfgdgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdedpfchdhdhahbgdgfg}
$$\begin{array}{c}(u1\_struct\_0~k7\_rsspace=k1\_rsspace){\unicdcdcdhd}(({\unicdcdadad} X0 .  (m1\_subset\_1~\\
X0~(u1\_struct\_0~k7\_rsspace)){\unicdbdjded}((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~\\
X0~k5\_numbers~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k5\_numbers~k1\_numbers)))))){\unicdcdcdhd}(({\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~\\
k7\_rsspace)){\unicdbdjdcd}(X0=k2\_rsspace~X0)){\unicdcdcdhd}(({\unicdcdadad} X0 .  (m1\_subset\_1~\\
X0~(u1\_struct\_0~k7\_rsspace)){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
k7\_rsspace)){\unicdbdjdcd}(k3\_rlvect\_1~k7\_rsspace~X0~X1=k1\_series\_1~k1\_numbers~\\
(k2\_rsspace~X0)~(k2\_rsspace~X1)))){\unicdcdcdhd}({\unicdcdadad} X0 .  (m1\_subset\_1~\\
X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~k7\_rsspace)){\unicdbdjdcd}\\
(k1\_rlvect\_1~k7\_rsspace~X1~X0=k26\_valued\_1~k5\_numbers~k1\_numbers~\\
(k2\_rsspace~X1)~X0))))))\end{array}$$
\end{theorem}
\end{document}
