\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{t22\_compos\_2 (TMS5zUKHF2sy7CJLj5J4TL6SU7DEYDc3n3e)}
\maketitle
Let $ v1\_amistd\_4 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_compos\_1 : {{\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 $ 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 $ 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 $ r2\_compos\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k63\_valued\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_compos\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
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}((k63\_valued\_1~X1=k63\_valued\_1~\\
X2){\unicdbdjdcd}(X1=X2))))\end{array}
\label{hyp:ehcdbdpfdgpgngahpgdhpfcd}
\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}(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)))))))){\unicdbdjdcd}((r1\_tarski~\\
(k63\_valued\_1~X1)~X2){\unicdbdjdcd}(r1\_tarski~(k63\_valued\_1~X1)~(k63\_valued\_1~\\
X2)))))\end{array}
\label{hyp:ehbdidpfdgpgngahpgdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_relat\_1~X0){\unicdcdcdhd}\\
((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finset\_1~X0))))){\unicdcdcdhd}\\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}\\
((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finset\_1~X1)))))){\unicdbdjdcd}((r2\_compos\_2~X0~X1){\unicdbdjded}\\
(r1\_compos\_2~X0~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfdgpgngahpgdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~\\
X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finset\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(r1\_compos\_2~X0~X1){\unicdbdjded}(r1\_tarski~(k63\_valued\_1~X0)~X1))\end{array}
\label{hyp:egedpfdgpgngahpgdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0}={X1}})}{\unicdbdjded}{({{({{{r1\_tarski}~{X0}}~{X1}})}{\unicdcdcdhd}{({{{r1\_tarski}~{X1}}~{X0}})}})}}}}\label{hyp:egbdadpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehcdcdpfdgpgngahpgdhpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_amistd\_4~X0){\unicdcdcdhd}(l1\_compos\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}\\
((v5\_relat\_1~X1~(u1\_compos\_1~X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_finset\_1~\\
X1){\unicdcdcdhd}((v1\_afinsq\_1~X1){\unicdcdcdhd}((v3\_compos\_1~X1~X0){\unicdcdcdhd}(v4\_compos\_1~X1~X0))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~\\
X2~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X2~(u1\_compos\_1~X0)){\unicdcdcdhd}((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_finset\_1~X2){\unicdcdcdhd}((v1\_afinsq\_1~X2){\unicdcdcdhd}((v3\_compos\_1~X2~X0){\unicdcdcdhd}\\
(v4\_compos\_1~X2~X0))))))))){\unicdbdjdcd}(((r2\_compos\_2~X1~X2){\unicdcdcdhd}(r2\_compos\_2~\\
X2~X1)){\unicdbdjdcd}(X1=X2))))\end{array}$$
\end{theorem}
\end{document}
