\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{t61\_compos\_2 (TMW7L8uqXoe7aL5vF1oRbp1RbrMpGsvCxxj)}
\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 $ v4\_compos\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_compos\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k11\_compos\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_compos\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_compos\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_compos\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_compos\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_compos\_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 $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_compos\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_compos\_1~\\
X0)){\unicdbdjdcd}(k10\_xtuple\_0~(k11\_compos\_1~X0~X1)=k7\_domain\_1~(u1\_compos\_1~\\
X0)~X1~(k2\_compos\_1~X0)))\end{array}
\label{hyp:ehgdhdpfdgpgngahpgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{r1\_tarski}~{k1\_xboole\_0}}~{X0}}}\label{hyp:ehcdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~X0){\unicdcdcdhd}(m1\_subset\_1~X2~X0))){\unicdbdjdcd}(k7\_domain\_1~X0~X1~X2=k2\_tarski~X1~\\
X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_compos\_0~X0){\unicdcdcdhd}(v5\_compos\_0~X0)){\unicdcdcdhd}\\
((v4\_compos\_0~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~X0))){\unicdbdjdcd}(v1\_xboole\_0~(k5\_xtuple\_0~\\
X1))\end{array}
\label{hyp:ggdgcdbdpfdgpgngahpgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_compos\_0~X0){\unicdcdcdhd}(v5\_compos\_0~X0)){\unicdbdjdcd}(v4\_compos\_0~\\
(k6\_compos\_0~X0)~X0)\end{array}
\label{hyp:ggdgcdadpfdgpgngahpgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xboole\_0}~{({{k10\_xtuple\_0}~{X0}})}})}}}\label{hyp:ggdgbdbdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_compos\_1~X0){\unicdbdjdcd}((v1\_compos\_0~(u1\_compos\_1~X0)){\unicdcdcdhd}\\
((v2\_compos\_0~(u1\_compos\_1~X0)){\unicdcdcdhd}((v3\_compos\_0~(u1\_compos\_1~\\
X0)){\unicdcdcdhd}(v5\_compos\_0~(u1\_compos\_1~X0)))))\end{array}
\label{hyp:egehpffhbdpfdgpgngahpgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_compos\_1~X0){\unicdbdjdcd}(m1\_subset\_1~(k2\_compos\_1~X0)~(u1\_compos\_1~\\
X0))\end{array}
\label{hyp:egehpflgcdpfdgpgngahpgdhpfbd}
\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}((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))))))\end{array}
\label{hyp:egehpflgbdbdpfdgpgngahpgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_amistd\_4~X0){\unicdcdcdhd}(l1\_compos\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((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))))){\unicdbdjdcd}((\\
v1\_compos\_2~X1~X0){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_compos\_1~X0)){\unicdbdjdcd}\\
((X2 \in k10\_xtuple\_0~X1){\unicdbdjdcd}(r1\_tarski~(k10\_xtuple\_0~(k5\_xtuple\_0~\\
X2))~(k9\_xtuple\_0~X1))))))\end{array}
\label{hyp:egfdpfdgpgngahpgdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k2\_tarski~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}((X3=X0){\unicdcdcdid}(X3=X1)))\end{array}
\label{hyp:egcdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_compos\_1~X0){\unicdbdjdcd}(k2\_compos\_1~X0=k6\_compos\_0~(u1\_compos\_1~\\
X0))\end{array}
\label{hyp:egbdadpfdgpgngahpgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v5\_compos\_0}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{X0}}}})}}}\label{hyp:dgdgcdpfdgpgngahpgdhpfad}
\end{equation}
\begin{theorem}\label{thm:ehgdbdpfdgpgngahpgdhpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_amistd\_4~X0){\unicdcdcdhd}(l1\_compos\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v6\_compos\_0~X1~(u1\_compos\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_compos\_1~\\
X0))){\unicdbdjdcd}((v4\_compos\_0~X1~(u1\_compos\_1~X0)){\unicdbdjdcd}(v1\_compos\_2~(k11\_compos\_1~\\
X0~X1)~X0)))\end{array}$$
\end{theorem}
\end{document}
