\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{t55\_monoid\_0 (TMV2EmPtoqGscC2xzjD18Bm1BPxt4Ero5bg)}
\maketitle
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_monoid\_0 : {\iota}$ be given.
Let $ k6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k24\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_monoid\_0 : {\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 $ m2\_monoid\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v22\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v15\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v17\_monoid\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_monoid\_0 : {\iota}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~k7\_monoid\_0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
k7\_monoid\_0)){\unicdbdjdcd}(((X0=X2){\unicdcdcdhd}(X1=X3)){\unicdbdjdcd}(k6\_algstr\_0~k7\_monoid\_0~\\
X2~X3=k24\_binop\_2~X0~X1)))))\end{array}
\label{hyp:ehfdddpfngpgogpgjgegpfad}
\end{equation}
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 .  (l3\_algstr\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_monoid\_0~X1~X0){\unicdbdjdcd}\\
(l3\_algstr\_0~X1))\end{array}
\label{hyp:egehpfngcdpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v2\_struct\_0~k8\_monoid\_0){\unicdcdcdhd}((v22\_algstr\_0~k8\_monoid\_0){\unicdcdcdhd}((\\
v4\_vectsp\_1~k8\_monoid\_0){\unicdcdcdhd}(m1\_monoid\_0~k8\_monoid\_0~k7\_monoid\_0)))\end{array}
\label{hyp:egehpflgidpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v2\_struct\_0~k7\_monoid\_0){\unicdcdcdhd}((v15\_algstr\_0~k7\_monoid\_0){\unicdcdcdhd}((\\
v1\_group\_1~k7\_monoid\_0){\unicdcdcdhd}((v17\_monoid\_0~k7\_monoid\_0){\unicdcdcdhd}(m2\_monoid\_0~\\
k7\_monoid\_0~k6\_monoid\_0))))\end{array}
\label{hyp:egehpflghdpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v2\_struct\_0~k6\_monoid\_0){\unicdcdcdhd}((v15\_algstr\_0~k6\_monoid\_0){\unicdcdcdhd}((\\
v1\_group\_1~k6\_monoid\_0){\unicdcdcdhd}((v3\_group\_1~k6\_monoid\_0){\unicdcdcdhd}((v5\_group\_1~\\
k6\_monoid\_0){\unicdcdcdhd}(l3\_algstr\_0~k6\_monoid\_0)))))\end{array}
\label{hyp:egehpflggdpfngpgogpgjgegpfad}
\end{equation}
\begin{theorem}\label{thm:ehfdfdpfngpgogpgjgegpfad}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~k8\_monoid\_0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
k8\_monoid\_0)){\unicdbdjdcd}(((X0=X2){\unicdcdcdhd}(X1=X3)){\unicdbdjdcd}(k6\_algstr\_0~k8\_monoid\_0~\\
X2~X3=k24\_binop\_2~X0~X1)))))\end{array}$$
\end{theorem}
\end{document}
