\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{t7\_compos\_2 (TMFYoCUB8bSxrYArs1J4xmtKZxSgBHqLrSp)}
\maketitle
Let $ v1\_amistd\_4 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_compos\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_compos\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_compos\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_compos\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_compos\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_compos\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_compos\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k11\_compos\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_compos\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_amistd\_4~X0){\unicdcdcdhd}(l1\_compos\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v6\_compos\_0~X1~(u1\_compos\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_compos\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v6\_compos\_0~X2~(u1\_compos\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(u1\_compos\_1~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}((v1\_relat\_1~\\
X3){\unicdcdcdhd}((v4\_relat\_1~X3~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X3~(u1\_compos\_1~\\
X0)){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_finset\_1~X3){\unicdcdcdhd}((v1\_afinsq\_1~X3){\unicdcdcdhd}\\
((v3\_compos\_1~X3~X0){\unicdcdcdhd}(v4\_compos\_1~X3~X0))))))))){\unicdbdjdcd}(k2\_compos\_2~\\
X0~(k1\_compos\_2~X0~X1~X3)~X2=k1\_compos\_2~X0~X1~(k2\_compos\_2~X0~X3~\\
X2)))))\end{array}
\label{hyp:ehfdpfdgpgngahpgdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_amistd\_4~X0){\unicdcdcdhd}(l1\_compos\_1~X0)){\unicdcdcdhd}\\
((v6\_compos\_0~X1~(u1\_compos\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_compos\_1~\\
X0)))){\unicdbdjdcd}((v1\_relat\_1~(k11\_compos\_1~X0~X1)){\unicdcdcdhd}((v4\_relat\_1~(k11\_compos\_1~\\
X0~X1)~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~(k11\_compos\_1~X0~X1)~(u1\_compos\_1~\\
X0)){\unicdcdcdhd}((v1\_funct\_1~(k11\_compos\_1~X0~X1)){\unicdcdcdhd}((v1\_finset\_1~(k11\_compos\_1~\\
X0~X1)){\unicdcdcdhd}((v3\_compos\_1~(k11\_compos\_1~X0~X1)~X0){\unicdcdcdhd}(v4\_compos\_1~(\\
k11\_compos\_1~X0~X1)~X0)))))))\end{array}
\label{hyp:ggdgbdpfdgpgngahpgdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_compos\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_compos\_1~\\
X0))){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k11\_compos\_1~X0~X1)){\unicdcdcdhd}((v1\_relat\_1~(k11\_compos\_1~\\
X0~X1)){\unicdcdcdhd}((v4\_relat\_1~(k11\_compos\_1~X0~X1)~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~\\
(k11\_compos\_1~X0~X1)~(u1\_compos\_1~X0)){\unicdcdcdhd}((v1\_funct\_1~(k11\_compos\_1~\\
X0~X1)){\unicdcdcdhd}((v1\_finset\_1~(k11\_compos\_1~X0~X1)){\unicdcdcdhd}(v1\_afinsq\_1~(k11\_compos\_1~\\
X0~X1))))))))\end{array}
\label{hyp:ggdgbdedpfdgpgngahpgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_amistd\_4~X0){\unicdcdcdhd}(l1\_compos\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v6\_compos\_0~X1~(u1\_compos\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_compos\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v6\_compos\_0~X2~(u1\_compos\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(u1\_compos\_1~X0))){\unicdbdjdcd}(k3\_compos\_2~X0~X1~X2=k8\_compos\_1~X0~(k11\_compos\_1~\\
X0~X1)~(k11\_compos\_1~X0~X2))))\end{array}
\label{hyp:egddpfdgpgngahpgdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_amistd\_4~X0){\unicdcdcdhd}(l1\_compos\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}\\
((v5\_relat\_1~X1~(u1\_compos\_1~X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_finset\_1~\\
X1){\unicdcdcdhd}((v1\_afinsq\_1~X1){\unicdcdcdhd}((v3\_compos\_1~X1~X0){\unicdcdcdhd}(v4\_compos\_1~X1~X0))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v6\_compos\_0~X2~(u1\_compos\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(u1\_compos\_1~X0))){\unicdbdjdcd}(k2\_compos\_2~X0~X1~X2=k8\_compos\_1~X0~X1~(\\
k11\_compos\_1~X0~X2))))\end{array}
\label{hyp:egcdpfdgpgngahpgdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_amistd\_4~X0){\unicdcdcdhd}(l1\_compos\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v6\_compos\_0~X1~(u1\_compos\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_compos\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~\\
X2~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X2~(u1\_compos\_1~X0)){\unicdcdcdhd}((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_finset\_1~X2){\unicdcdcdhd}((v1\_afinsq\_1~X2){\unicdcdcdhd}((v3\_compos\_1~X2~X0){\unicdcdcdhd}\\
(v4\_compos\_1~X2~X0))))))))){\unicdbdjdcd}(k1\_compos\_2~X0~X1~X2=k8\_compos\_1~\\
X0~(k11\_compos\_1~X0~X1)~X2)))\end{array}
\label{hyp:egbdpfdgpgngahpgdhpfcd}
\end{equation}
\begin{theorem}\label{thm:ehhdpfdgpgngahpgdhpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_amistd\_4~X0){\unicdcdcdhd}(l1\_compos\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v6\_compos\_0~X1~(u1\_compos\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_compos\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v6\_compos\_0~X2~(u1\_compos\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(u1\_compos\_1~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v6\_compos\_0~X3~(u1\_compos\_1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X3~(u1\_compos\_1~X0))){\unicdbdjdcd}(k2\_compos\_2~X0~(k3\_compos\_2~\\
X0~X1~X2)~X3=k1\_compos\_2~X0~X1~(k3\_compos\_2~X0~X2~X3)))))\end{array}$$
\end{theorem}
\end{document}
