\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{t62\_monoid\_0 (TMFwCj5zo1xcWr8TNdjVwzaA5tYRQJUvNkd)}
\maketitle
Let $ v1\_xboole\_0 : {{\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 $ k10\_monoid\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_monoid\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_monoid\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v15\_algstr\_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 $ v2\_monoid\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v16\_monoid\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v17\_monoid\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v22\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_finseq\_2 : {{\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}({\unicdcdadad} X1 .  \\
(m1\_monoid\_0~X1~X0){\unicdbdjdcd}((u1\_struct\_0~X1=u1\_struct\_0~X0){\unicdcdcdhd}((r1\_funct\_2~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~X1))~(u1\_struct\_0~\\
X1)~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(u1\_struct\_0~\\
X0)~(u2\_algstr\_0~X1)~(u2\_algstr\_0~X0)){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}(((X2=X4){\unicdcdcdhd}(X3=X5)){\unicdbdjdcd}(k6\_algstr\_0~\\
X1~X2~X3=k6\_algstr\_0~X0~X4~X5)))))))))\end{array}
\label{hyp:ehbdidpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k9\_monoid\_0~X0)){\unicdcdcdhd}\\
((v15\_algstr\_0~(k9\_monoid\_0~X0)){\unicdcdcdhd}((v1\_group\_1~(k9\_monoid\_0~\\
X0)){\unicdcdcdhd}((v3\_group\_1~(k9\_monoid\_0~X0)){\unicdcdcdhd}((v2\_monoid\_0~(k9\_monoid\_0~\\
X0)){\unicdcdcdhd}((v16\_monoid\_0~(k9\_monoid\_0~X0)){\unicdcdcdhd}((v17\_monoid\_0~(k9\_monoid\_0~\\
X0)){\unicdcdcdhd}(l3\_algstr\_0~(k9\_monoid\_0~X0)))))))))\end{array}
\label{hyp:egehpflgjdpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k10\_monoid\_0~X0)){\unicdcdcdhd}\\
((v22\_algstr\_0~(k10\_monoid\_0~X0)){\unicdcdcdhd}((v4\_vectsp\_1~(k10\_monoid\_0~\\
X0)){\unicdcdcdhd}(m1\_monoid\_0~(k10\_monoid\_0~X0)~(k9\_monoid\_0~X0)))))\end{array}
\label{hyp:egehpflgbdadpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v15\_algstr\_0~X1){\unicdcdcdhd}((v1\_group\_1~X1){\unicdcdcdhd}((v3\_group\_1~X1){\unicdcdcdhd}((v2\_monoid\_0~\\
X1){\unicdcdcdhd}((v16\_monoid\_0~X1){\unicdcdcdhd}((v17\_monoid\_0~X1){\unicdcdcdhd}(l3\_algstr\_0~X1)))))))){\unicdbdjdcd}\\
((X1=k9\_monoid\_0~X0){\unicdbdjded}((u1\_struct\_0~X1=k3\_finseq\_2~X0){\unicdcdcdhd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X1)){\unicdbdjdcd}(k6\_algstr\_0~X1~X2~X3=k7\_finseq\_1~X2~X3))))))\end{array}
\label{hyp:egddedpfngpgogpgjgegpfad}
\end{equation}
\begin{theorem}\label{thm:ehgdcdpfngpgogpgjgegpfad}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
(k10\_monoid\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
(k10\_monoid\_0~X0))){\unicdbdjdcd}(k6\_algstr\_0~(k10\_monoid\_0~X0)~X1~X2=k7\_finseq\_1~\\
X1~X2)))\end{array}$$
\end{theorem}
\end{document}
