\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{t4\_msualg\_8 (TMNj7aQvL2MtKbAC2RoAMccUruVFsKCNFhi)}
\maketitle
Let $ k6\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_msualg\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r3\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v10\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v14\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v15\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k2\_msualg\_5~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k2\_msualg\_5~\\
X0))){\unicdbdjdcd}((r3\_lattices~(k2\_msualg\_5~X0)~X1~X2){\unicdbdjded}(r1\_tarski~X1~X2)))\end{array}
\label{hyp:ehfdpfmgbgehehjgdgfgfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_relat\_2~(k1\_eqrel\_1~X0)){\unicdcdcdhd}((v8\_relat\_2~(k1\_eqrel\_1~\\
X0)){\unicdcdcdhd}((v1\_partfun1~(k1\_eqrel\_1~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~(k1\_eqrel\_1~\\
X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))))\end{array}
\label{hyp:ehedpffgbhchfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~X1)){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddpfdhfhcgdhfgeh}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X0 \in u1\_struct\_0~(k2\_msualg\_5~X1)){\unicdbdjded}((v1\_partfun1~\\
X0~X1){\unicdcdcdhd}((v3\_relat\_2~X0){\unicdcdcdhd}((v8\_relat\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X1~X1))))))\end{array}
\label{hyp:ehcdbdpfngdhfhbgmghgpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}((v14\_lattices~\\
X0){\unicdcdcdhd}(l3\_lattices~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(r3\_lattices~X0~X1~(k6\_lattices~X0)))\end{array}
\label{hyp:ehbdjdpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r1\_tarski}~{X0}}~{X0}}}}\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdgcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v2\_struct\_0~(k2\_msualg\_5~X0)){\unicdcdcdhd}((v3\_lattices~(k2\_msualg\_5~\\
X0)){\unicdcdcdhd}((v10\_lattices~(k2\_msualg\_5~X0)){\unicdcdcdhd}(v15\_lattices~(k2\_msualg\_5~\\
X0))))\end{array}
\label{hyp:ggdgbdpfngdhfhbgmghgpfid}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l3\_lattices}~{X0}})}{\unicdbdjdcd}{({{({{l1\_lattices}~{X0}})}{\unicdcdcdhd}{({{l2\_lattices}~{X0}})}})}}}\label{hyp:egehpfmgddpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_lattices}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_lattices~X0)){\unicdbdjdcd}(m1\_subset\_1~\\
(k6\_lattices~X0)~(u1\_struct\_0~X0))\end{array}
\label{hyp:egehpflggdpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v2\_struct\_0~(k2\_msualg\_5~X0)){\unicdcdcdhd}((v3\_lattices~(k2\_msualg\_5~\\
X0)){\unicdcdcdhd}((v10\_lattices~(k2\_msualg\_5~X0)){\unicdcdcdhd}(l3\_lattices~(k2\_msualg\_5~\\
X0))))\end{array}
\label{hyp:egehpflgcdpfngdhfhbgmghgpffd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k1\_eqrel\_1}~{X0}}={{{k2\_zfmisc\_1}~{X0}}~{X0}}}}\label{hyp:egbdpffgbhchfgmgpfbd}
\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}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_lattices~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v15\_lattices~\\
X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_lattices~X0){\unicdcdcdhd}(v14\_lattices~X0))))\end{array}
\label{hyp:dgdgedpfmgbgehehjgdgfgdh}
\end{equation}
\begin{theorem}\label{thm:ehedpfngdhfhbgmghgpfid}
${{\unicdcdadad} X0 .  {{{k6\_lattices}~{({{k2\_msualg\_5}~{X0}})}}={{k1\_eqrel\_1}~{X0}}}}$.
\end{theorem}
\end{document}
