\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{t36\_compos\_2 (TMXR2K6GieJWNnosqKeTA522t99RiawKCKZ)}
\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 $ 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 $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_compos\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k11\_compos\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k62\_valued\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r2\_compos\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k8\_compos\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ np\_\_0 : {\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}(k1\_funct\_1~(k11\_compos\_1~X0~X1)~k6\_numbers=X1))\end{array}
\label{hyp:ehfdidpfdgpgngahpgdhpfbd}
\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}(k62\_valued\_1~(k11\_compos\_1~X0~X1)=np\_\_1))\end{array}
\label{hyp:ehddadpfdgpgngahpgdhpfcd}
\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 .  ((\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}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}((\\
r2\_compos\_2~X1~X2){\unicdbdjdcd}((r1\_xxreal\_0~(k62\_valued\_1~X1)~X3){\unicdcdcdid}(k1\_funct\_1~\\
X1~X3=k1\_funct\_1~X2~X3))))))\end{array}
\label{hyp:ehcdidpfdgpgngahpgdhpfcd}
\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 .  ((\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}(r2\_compos\_2~X1~(k8\_compos\_1~X0~X1~\\
X2))))\end{array}
\label{hyp:ehcdddpfdgpgngahpgdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k1\_xboole\_0}}~{k4\_ordinal1}}\label{hyp:ehbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{np\_\_0}}\label{hyp:dhahdgadpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_1}}~{np\_\_0}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdpfchad}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\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 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((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))){\unicdcdcdhd}((\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}\\
((\preoh v1\_xboole\_0~(k1\_compos\_2~X0~X1~X2)){\unicdcdcdhd}((v1\_relat\_1~(k1\_compos\_2~\\
X0~X1~X2)){\unicdcdcdhd}((v4\_relat\_1~(k1\_compos\_2~X0~X1~X2)~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~\\
(k1\_compos\_2~X0~X1~X2)~(u1\_compos\_1~X0)){\unicdcdcdhd}((v1\_funct\_1~(k1\_compos\_2~\\
X0~X1~X2)){\unicdcdcdhd}((v1\_finset\_1~(k1\_compos\_2~X0~X1~X2)){\unicdcdcdhd}((v1\_afinsq\_1~\\
(k1\_compos\_2~X0~X1~X2)){\unicdcdcdhd}((v3\_compos\_1~(k1\_compos\_2~X0~X1~X2)~X0){\unicdcdcdhd}\\
(v4\_compos\_1~(k1\_compos\_2~X0~X1~X2)~X0)))))))))\end{array}
\label{hyp:egehpflgbdpfdgpgngahpgdhpfcd}
\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 .  \\
((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}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehddgdpfdgpgngahpgdhpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_amistd\_4~X0){\unicdcdcdhd}(l1\_compos\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v6\_compos\_0~X1~(u1\_compos\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_compos\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~\\
X2~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X2~(u1\_compos\_1~X0)){\unicdcdcdhd}((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_finset\_1~X2){\unicdcdcdhd}((v1\_afinsq\_1~X2){\unicdcdcdhd}((v3\_compos\_1~X2~X0){\unicdcdcdhd}\\
(v4\_compos\_1~X2~X0))))))))){\unicdbdjdcd}(k1\_funct\_1~(k1\_compos\_2~X0~X1~X2)~\\
k6\_numbers=X1)))\end{array}$$
\end{theorem}
\end{document}
