\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{l1\_algstr\_2 (TMbWWBmf3rUhcrqj9BJbbCGD9Cbi1qB3M4T)}
\maketitle
Let $ k6\_numbers : {\iota}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_vectsp\_1 : {\iota}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k5\_complex1 : {\iota}$ 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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ g6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ l6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l5\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k35\_binop\_2 : {\iota}$ be given.
Let $ k33\_binop\_2 : {\iota}$ be given.
Let $ v36\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_complex1}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfdgpgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k6\_numbers}}~{k1\_numbers}}\label{hyp:mgbdjdpfbgchjhehngpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~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}((m1\_subset\_1~X3~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X4~X0)))){\unicdbdjdcd}({\unicdcdadad} X5 .  {\unicdcdadad} X6 .  {\unicdcdadad} X7 .  {\unicdcdadad} X8 .  \\
{\unicdcdadad} X9 .  (g6\_algstr\_0~X0~X1~X2~X3~X4=g6\_algstr\_0~X5~X6~X7~X8~X9){\unicdbdjdcd}\\
((X0=X5){\unicdcdcdhd}((X1=X6){\unicdcdcdhd}((X2=X7){\unicdcdcdhd}((X3=X8){\unicdcdcdhd}(X4=X9))))))\end{array}
\label{hyp:ggchfgfgpfhggdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l6\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l2\_algstr\_0}~{X0}})}{\unicdcdcdhd}{({{l5\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmggdpfbgmghgdhehchpfad}
\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}
\begin{array}{c}(v1\_funct\_1~k35\_binop\_2){\unicdcdcdhd}((v1\_funct\_2~k35\_binop\_2~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~k35\_binop\_2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)~\\
k1\_numbers))))\end{array}
\label{hyp:egehpflgddfdpfcgjgogpgahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k33\_binop\_2){\unicdcdcdhd}((v1\_funct\_2~k33\_binop\_2~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~k33\_binop\_2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)~\\
k1\_numbers))))\end{array}
\label{hyp:egehpflgddddpfcgjgogpgahpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{({{v36\_algstr\_0}~{k2\_vectsp\_1}})}{\unicdcdcdhd}{({{l6\_algstr\_0}~{k2\_vectsp\_1}})}}\label{hyp:egehpflgcdpfghfgdgehdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{{k4\_struct\_0}~{X0}}={{u2\_struct\_0}~{X0}}})}}}\label{hyp:eggdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k2\_vectsp\_1=g6\_algstr\_0~k1\_numbers~k33\_binop\_2~k35\_binop\_2~\\
np\_\_1~k6\_numbers\end{array}
\label{hyp:egfdpfghfgdgehdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l6\_algstr\_0~X0){\unicdbdjdcd}((v36\_algstr\_0~X0){\unicdbdjdcd}(X0=g6\_algstr\_0~\\
(u1\_struct\_0~X0)~(u1\_algstr\_0~X0)~(u2\_algstr\_0~X0)~(u3\_struct\_0~\\
X0)~(u2\_struct\_0~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghddgdpfbgmghgdhehchpfad}
\end{equation}
\begin{theorem}\label{thm:mgbdpfbgmghgdhehchpfcd}
${{k6\_numbers}={{k4\_struct\_0}~{k2\_vectsp\_1}}}$.
\end{theorem}
\end{document}
