\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t43\_compos\_1 (TMTBb5uRPNRHDSC9padmth5RsV53Xqxu6Am)}
\maketitle
Let $ l1\_compos\_1 : {{\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 $ u1\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_compos\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k61\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_compos\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_compos\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  ((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))))){\unicdbdjdcd}(k61\_valued\_1~(k5\_compos\_1~X0~X3~X1)~\\
X2=k5\_compos\_1~X0~(k61\_valued\_1~X3~X2)~X1))))\end{array}
\label{hyp:ehddedpfdgpgngahpgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~X2)){\unicdbdjdcd}(k61\_valued\_1~(k61\_valued\_1~\\
X2~X1)~X0=k61\_valued\_1~X2~(k2\_xcmplx\_0~X1~X0))))\end{array}
\label{hyp:ehcdbdpfghbgmgfhfgegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(l1\_compos\_1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((v4\_relat\_1~\\
X3~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X3~(u1\_compos\_1~X2)){\unicdcdcdhd}((v1\_funct\_1~\\
X3){\unicdcdcdhd}(v1\_finset\_1~X3))))){\unicdbdjdcd}(k5\_compos\_1~X2~(k5\_compos\_1~X2~X3~X0)~\\
X1=k5\_compos\_1~X2~X3~(k2\_xcmplx\_0~X0~X1)))))\end{array}
\label{hyp:ehbdhdpfdgpgngahpgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}(\\
v7\_ordinal1~(k2\_xcmplx\_0~X0~X1))\end{array}
\label{hyp:ggdgbdpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdcdcdhd}(v7\_ordinal1~\\
X1)){\unicdbdjdcd}((v1\_relat\_1~(k61\_valued\_1~X0~X1)){\unicdcdcdhd}((v4\_relat\_1~(k61\_valued\_1~\\
X0~X1)~k5\_numbers){\unicdcdcdhd}(v1\_funct\_1~(k61\_valued\_1~X0~X1))))\end{array}
\label{hyp:ggdgbdadddpfghbgmgfhfgegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((l1\_compos\_1~X0){\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}(v7\_ordinal1~X2))){\unicdbdjdcd}\\
((v1\_relat\_1~(k6\_compos\_1~X0~X1~X2)){\unicdcdcdhd}((v4\_relat\_1~(k6\_compos\_1~\\
X0~X1~X2)~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~(k6\_compos\_1~X0~X1~X2)~(u1\_compos\_1~\\
X0)){\unicdcdcdhd}((v1\_funct\_1~(k6\_compos\_1~X0~X1~X2)){\unicdcdcdhd}(v1\_finset\_1~(k6\_compos\_1~\\
X0~X1~X2))))))\end{array}
\label{hyp:egehpflggdpfdgpgngahpgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdcdcdhd}(v7\_ordinal1~\\
X1)){\unicdbdjdcd}((v1\_relat\_1~(k61\_valued\_1~X0~X1)){\unicdcdcdhd}(v1\_funct\_1~(k61\_valued\_1~\\
X0~X1)))\end{array}
\label{hyp:egehpflggdbdpfghbgmgfhfgegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((l1\_compos\_1~X0){\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}(v7\_ordinal1~X2))){\unicdbdjdcd}\\
((v1\_relat\_1~(k5\_compos\_1~X0~X1~X2)){\unicdcdcdhd}((v4\_relat\_1~(k5\_compos\_1~\\
X0~X1~X2)~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~(k5\_compos\_1~X0~X1~X2)~(u1\_compos\_1~\\
X0)){\unicdcdcdhd}((v1\_funct\_1~(k5\_compos\_1~X0~X1~X2)){\unicdcdcdhd}(v1\_finset\_1~(k5\_compos\_1~\\
X0~X1~X2))))))\end{array}
\label{hyp:egehpflgfdpfdgpgngahpgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (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}({\unicdcdadad} X2 .  (v7\_ordinal1~\\
X2){\unicdbdjdcd}(k6\_compos\_1~X0~X1~X2=k61\_valued\_1~(k5\_compos\_1~X0~X1~X2)~X2)))\end{array}
\label{hyp:egcdcdpfdgpgngahpgdhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedddpfdgpgngahpgdhpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (l1\_compos\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((\\
v4\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X1~(u1\_compos\_1~X0)){\unicdcdcdhd}\\
((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finset\_1~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (v7\_ordinal1~\\
X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}(k6\_compos\_1~X0~(k6\_compos\_1~\\
X0~X1~X2)~X3=k6\_compos\_1~X0~X1~(k2\_xcmplx\_0~X2~X3)))))\end{array}$$
\end{theorem}
\end{document}
