\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{t91\_scmfsa\_2 (TMdG7dQxmN8t4aNQfZRuitRgGYb2VtH8p4h)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_scmfsa\_2 : {\iota}$ be given.
Let $ k3\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v2\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ k1\_ami\_3 : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ v1\_ami\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_ami\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_ami\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_ami\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_ami\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_ami\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_ami\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_ami\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_ami\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_ami\_3)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdbdjdcd}(((X0=X1){\unicdcdcdhd}(v2\_extpro\_1~\\
X0~np\_\_2~k1\_ami\_3)){\unicdbdjdcd}(v2\_extpro\_1~X1~np\_\_3~k1\_scmfsa\_2)))\end{array}
\label{hyp:ehhdhdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_ami\_3)){\unicdbdjded}(\preoh (X0{\unicdcdgdad}k3\_xtuple\_0~\\
k6\_numbers~k1\_xboole\_0~k1\_xboole\_0){\unicdcdcdhd}(({\unicdcdadad} X1 .  ((v1\_ami\_2~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_ami\_3))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\\
v1\_ami\_2~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~k1\_ami\_3))){\unicdbdjdcd}(X0{\unicdcdgdad}k2\_ami\_3~\\
X1~X2))){\unicdcdcdhd}(({\unicdcdadad} X1 .  ((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~\\
k1\_ami\_3))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_ami\_2~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~\\
k1\_ami\_3))){\unicdbdjdcd}(X0{\unicdcdgdad}k3\_ami\_3~X1~X2))){\unicdcdcdhd}(({\unicdcdadad} X1 .  ((v1\_ami\_2~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(u1\_struct\_0~k1\_ami\_3))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_ami\_2~\\
X2){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~k1\_ami\_3))){\unicdbdjdcd}(X0{\unicdcdgdad}k4\_ami\_3~X1~\\
X2))){\unicdcdcdhd}(({\unicdcdadad} X1 .  ((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~\\
k1\_ami\_3))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_ami\_2~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~\\
k1\_ami\_3))){\unicdbdjdcd}(X0{\unicdcdgdad}k5\_ami\_3~X1~X2))){\unicdcdcdhd}(({\unicdcdadad} X1 .  ((v1\_ami\_2~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(u1\_struct\_0~k1\_ami\_3))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_ami\_2~\\
X2){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~k1\_ami\_3))){\unicdbdjdcd}(X0{\unicdcdgdad}k6\_ami\_3~X1~\\
X2))){\unicdcdcdhd}(({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}(X0{\unicdcdgdad}k7\_ami\_3~X1)){\unicdcdcdhd}(({\unicdcdadad} X1 .  \\
((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_ami\_3))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}(X0{\unicdcdgdad}k8\_ami\_3~X2~X1))){\unicdcdcdhd}({\unicdcdadad} X1 .  ((v1\_ami\_2~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_ami\_3))){\unicdbdjdcd}({\unicdcdadad} X2 .  (v7\_ordinal1~\\
X2){\unicdbdjdcd}(X0{\unicdcdgdad}k9\_ami\_3~X2~X1)))))))))))\end{array}
\label{hyp:mgddbdpfbgngjgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_ami\_3)){\unicdbdjdcd}((X0=k3\_xtuple\_0~\\
k6\_numbers~k1\_xboole\_0~k1\_xboole\_0){\unicdbdjdcd}(v2\_extpro\_1~X0~np\_\_2~k1\_ami\_3))\end{array}
\label{hyp:mgcdcdpfbgngjgpfdd}
\end{equation}
\begin{theorem}\label{thm:ehjdbdpfdhdgngggdhbgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdbdjdcd}((X0=\\
k3\_xtuple\_0~k6\_numbers~k1\_xboole\_0~k1\_xboole\_0){\unicdbdjdcd}(v2\_extpro\_1~\\
X0~np\_\_3~k1\_scmfsa\_2))\end{array}$$
\end{theorem}
\end{document}
