\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{t13\_polyalg1 (TMQKQh5Y7T5XYesWd4qUT9WNvbt8v8JPMWA)}
\maketitle
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_polyalg1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_polyalg1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ g1\_polyalg1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ u2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_vectsp\_1 : {{\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 $ l4\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l4\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_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 $ l1\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_realset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_polyalg1~X1~X0){\unicdbdjdcd}\\
(m1\_polyalg1~X1~X0~X1))\end{array}
\label{hyp:ehbdbdpfahpgmgjhbgmghgbd}
\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 .  {{({{l5\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l4\_algstr\_0}~{X0}})}{\unicdcdcdhd}{({{l4\_struct\_0}~{X0}})}})}}}\label{hyp:egehpfmgfdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l4\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l3\_struct\_0}~{X0}})}{\unicdcdcdhd}{({{l3\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmgedpfbgmghgdhehchpfad}
\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}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_polyalg1~X1~X0){\unicdbdjdcd}\\
((l6\_algstr\_0~X1){\unicdcdcdhd}(l1\_vectsp\_1~X1~X0)))\end{array}
\label{hyp:egehpfmgbdpfahpgmgjhbgmghgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l3\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{{k5\_struct\_0}~{X0}}={{u3\_struct\_0}~{X0}}})}}}\label{hyp:eghdpfdhehchfhdgehpfad}
\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}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_polyalg1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (l1\_polyalg1~X2~X0){\unicdbdjdcd}((m1\_polyalg1~X2~X0~X1){\unicdbdjded}((r1\_tarski~\\
(u1\_struct\_0~X2)~(u1\_struct\_0~X1)){\unicdcdcdhd}((k5\_struct\_0~X2=k5\_struct\_0~\\
X1){\unicdcdcdhd}((k4\_struct\_0~X2=k4\_struct\_0~X1){\unicdcdcdhd}((u1\_algstr\_0~X2=k1\_realset1~\\
(u1\_algstr\_0~X1)~(u1\_struct\_0~X2)){\unicdcdcdhd}((u2\_algstr\_0~X2=k1\_realset1~\\
(u2\_algstr\_0~X1)~(u1\_struct\_0~X2)){\unicdcdcdhd}(u1\_vectsp\_1~X0~X2=k2\_partfun1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1))~(u1\_struct\_0~\\
X1)~(u1\_vectsp\_1~X0~X1)~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X2)))))))))))\end{array}
\label{hyp:egddpfahpgmgjhbgmghgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0}={X1}})}{\unicdbdjded}{({{({{{r1\_tarski}~{X0}}~{X1}})}{\unicdcdcdhd}{({{{r1\_tarski}~{X1}}~{X0}})}})}}}}\label{hyp:egbdadpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdddpfahpgmgjhbgmghgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_polyalg1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (l1\_polyalg1~X2~X0){\unicdbdjdcd}(((m1\_polyalg1~X1~X0~X2){\unicdcdcdhd}(m1\_polyalg1~\\
X2~X0~X1)){\unicdbdjdcd}(g1\_polyalg1~X0~(u1\_struct\_0~X1)~(u1\_algstr\_0~X1)~(u2\_algstr\_0~\\
X1)~(u2\_struct\_0~X1)~(u3\_struct\_0~X1)~(u1\_vectsp\_1~X0~X1)=g1\_polyalg1~\\
X0~(u1\_struct\_0~X2)~(u1\_algstr\_0~X2)~(u2\_algstr\_0~X2)~(u2\_struct\_0~\\
X2)~(u3\_struct\_0~X2)~(u1\_vectsp\_1~X0~X2)))))\end{array}$$
\end{theorem}
\end{document}
