\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{t32\_quantal1 (TMFDs8xNpeDNfSo7NAmbRNNKWwP5gWJyqXC)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v10\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_quantal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_quantal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v20\_quantal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v21\_quantal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_quantal1 : {{\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\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_quantal1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l3\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l1\_quantal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v17\_quantal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_quantal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_quantal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_quantal1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l2\_quantal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l4\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_quantal1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l3\_algstr\_0~X0)){\unicdbdjdcd}((v1\_group\_1~\\
X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}((k6\_algstr\_0~\\
X0~(k4\_binop\_1~(u1\_struct\_0~X0)~(u2\_algstr\_0~X0))~X1=X1){\unicdcdcdhd}(k6\_algstr\_0~\\
X0~X1~(k4\_binop\_1~(u1\_struct\_0~X0)~(u2\_algstr\_0~X0))=X1))))\end{array}
\label{hyp:ehfdpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v10\_lattices~\\
X0){\unicdcdcdhd}((v4\_lattice3~X0){\unicdcdcdhd}((v7\_quantal1~X0){\unicdcdcdhd}((v8\_quantal1~X0){\unicdcdcdhd}\\
(l1\_quantal1~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}((v17\_quantal1~X1~X0){\unicdbdjdcd}((v1\_group\_1~X0){\unicdcdcdhd}((k4\_binop\_1~(u1\_struct\_0~\\
X0)~(u2\_algstr\_0~X0)=k1\_quantal1~X0~X1~X1){\unicdcdcdhd}(k4\_binop\_1~(u1\_struct\_0~\\
X0)~(u2\_algstr\_0~X0)=k2\_quantal1~X0~X1~X1)))))\end{array}
\label{hyp:ehbdjdpfbhfhbgogehbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_quantal1~X0){\unicdbdjdcd}(m1\_subset\_1~(u1\_quantal1~X0)~(u1\_struct\_0~\\
X0))\end{array}
\label{hyp:egehpffhbdpfbhfhbgogehbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l3\_quantal1}~{X0}})}{\unicdbdjdcd}{({{l2\_quantal1}~{X0}})}}}\label{hyp:egehpfmgddpfbhfhbgogehbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_quantal1}~{X0}})}{\unicdbdjdcd}{({{({{l1\_quantal1}~{X0}})}{\unicdcdcdhd}{({{l4\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmgcdpfbhfhbgogehbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_quantal1}~{X0}})}{\unicdbdjdcd}{({{({{l3\_lattices}~{X0}})}{\unicdcdcdhd}{({{l3\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmgbdpfbhfhbgogehbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l3\_quantal1~X0)){\unicdbdjdcd}(k4\_quantal1~\\
X0=k1\_quantal1~X0~(k3\_quantal1~X0)~(k3\_quantal1~X0))\end{array}
\label{hyp:egcdcdpfbhfhbgogehbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l3\_quantal1}~{X0}})}{\unicdbdjdcd}{({{{k3\_quantal1}~{X0}}={{u1\_quantal1}~{X0}}})}}}\label{hyp:egcdbdpfbhfhbgogehbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l3\_quantal1~X0)){\unicdbdjdcd}((v21\_quantal1~\\
X0){\unicdbdjded}(v17\_quantal1~(u1\_quantal1~X0)~X0))\end{array}
\label{hyp:egcdadpfbhfhbgogehbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehddcdpfbhfhbgogehbgmgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}((v4\_lattice3~X0){\unicdcdcdhd}((v7\_quantal1~X0){\unicdcdcdhd}\\
((v8\_quantal1~X0){\unicdcdcdhd}((v20\_quantal1~X0){\unicdcdcdhd}((v21\_quantal1~X0){\unicdcdcdhd}(l3\_quantal1~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
((k6\_algstr\_0~X0~X1~(k4\_quantal1~X0)=X1){\unicdcdcdhd}(k6\_algstr\_0~X0~(k4\_quantal1~\\
X0)~X1=X1)))\end{array}$$
\end{theorem}
\end{document}
