\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{l68\_o\_ring\_1 (TMHpgbbHXQXHKkNEa64iE4Uyku5zruehyNQ)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v6\_o\_ring\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v13\_o\_ring\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v10\_o\_ring\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_finseq\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}((v10\_o\_ring\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}((r1\_xxreal\_0~X2~(k3\_finseq\_1~X1)){\unicdbdjdcd}((X2=k6\_numbers){\unicdcdcdid}\\
(v13\_o\_ring\_1~(k7\_partfun1~(u1\_struct\_0~X0)~X1~X2)~X0))))))\end{array}
\label{hyp:mgfdidpfpgpfchjgoghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_finseq\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}((v6\_o\_ring\_1~X1~X0){\unicdbdjdcd}(v10\_o\_ring\_1~\\
X1~X0)))\end{array}
\label{hyp:mgddidpfpgpfchjgoghgpfbd}
\end{equation}
\begin{theorem}\label{thm:mggdidpfpgpfchjgoghgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
(l6\_algstr\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~(u1\_struct\_0~X1)){\unicdbdjdcd}\\
(((v6\_o\_ring\_1~X2~X1){\unicdcdcdhd}(r1\_xxreal\_0~X0~(k3\_finseq\_1~X2))){\unicdbdjdcd}((k6\_numbers=\\
X0){\unicdcdcdid}(v13\_o\_ring\_1~(k7\_partfun1~(u1\_struct\_0~X1)~X2~X0)~X1)))))\end{array}$$
\end{theorem}
\end{document}
