\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{t5\_compos\_0 (TMTJZH8BfDy9uphjnpsKCw4ZmFPZakLxort)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_compos\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_compos\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_compos\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_compos\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_compos\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_compos\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_compos\_0~\\
X0){\unicdcdcdhd}((v2\_compos\_0~X0){\unicdcdcdhd}(v3\_compos\_0~X0)))){\unicdcdcdhd}((m1\_subset\_1~X1~\\
X0){\unicdcdcdhd}(v7\_ordinal1~X2))){\unicdbdjdcd}(m1\_subset\_1~(k5\_compos\_0~X0~X1~X2)~X0)\end{array}
\label{hyp:egehpflgfdpfdgpgngahpgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_compos\_0~X0){\unicdcdcdhd}((v2\_compos\_0~\\
X0){\unicdcdcdhd}(v3\_compos\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~X0){\unicdbdjdcd}((X3=k5\_compos\_0~\\
X0~X1~X2){\unicdbdjded}((k2\_compos\_0~X0~X3=k2\_compos\_0~X0~X1){\unicdcdcdhd}((k2\_xtuple\_0~\\
X3=k2\_xtuple\_0~X1){\unicdcdcdhd}(k5\_xtuple\_0~X3=k7\_valued\_1~(k5\_xtuple\_0~\\
X1)~X2)))))))\end{array}
\label{hyp:egjdpfdgpgngahpgdhpfad}
\end{equation}
\begin{theorem}\label{thm:ehfdpfdgpgngahpgdhpfad}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
((v1\_compos\_0~X1){\unicdcdcdhd}((v2\_compos\_0~X1){\unicdcdcdhd}(v3\_compos\_0~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~X1){\unicdbdjdcd}(k3\_compos\_0~X1~(k2\_compos\_0~X1~X2)=k3\_compos\_0~\\
X1~(k2\_compos\_0~X1~(k5\_compos\_0~X1~X2~X0)))))\end{array}$$
\end{theorem}
\end{document}
