\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{t29\_circcmb3 (TMFjhKngc1RmXwhpQAgEHVwdhW3NxbUeRqu)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_circcmb3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_circcmb3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v4\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r2\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v4\_msafree2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_circcomb : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_circcomb : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_circcomb : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u4\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v4\_msualg\_1~\\
X2~X0){\unicdcdcdhd}(l3\_msualg\_1~X2~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v4\_msualg\_1~X3~X1){\unicdcdcdhd}\\
(l3\_msualg\_1~X3~X1)){\unicdbdjdcd}(((v4\_circcomb~X2~X0){\unicdcdcdhd}((v4\_circcomb~X3~X1){\unicdcdcdhd}\\
(r1\_partfun1~(u3\_msualg\_1~X0~X2)~(u3\_msualg\_1~X1~X3)))){\unicdbdjdcd}(v4\_circcomb~\\
(k3\_circcomb~X0~X1~X2~X3)~(k2\_circcomb~X0~X1))))))\end{array}
\label{hyp:ehgdddpfdgjgchdgdgpgngcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_circcmb3~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_circcmb3~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m2\_circcmb3~X3~X0~X1){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_circcmb3~X4~X0~X2){\unicdbdjdcd}(r2\_circcomb~\\
X1~X2~X3~X4)))))\end{array}
\label{hyp:ehcdhdpfdgjgchdgdgngcgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdcdcdhd}\\
(m1\_circcmb3~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_circcmb3~X2~X0~X1){\unicdbdjdcd}((v4\_msafree2~\\
X2~X1){\unicdcdcdhd}(l3\_msualg\_1~X2~X1)))\end{array}
\label{hyp:egehpfngcdpfdgjgchdgdgngcgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_circcmb3~X1~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((\preoh v11\_struct\_0~X1){\unicdcdcdhd}\\
((v1\_circcomb~X1){\unicdcdcdhd}((v2\_circcomb~X1){\unicdcdcdhd}((v5\_circcomb~X1){\unicdcdcdhd}(l1\_msualg\_1~\\
X1)))))))\end{array}
\label{hyp:egehpfngbdpfdgjgchdgdgngcgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  (l3\_msualg\_1~\\
X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (l3\_msualg\_1~X3~X1){\unicdbdjdcd}((r2\_circcomb~X0~X1~X2~X3){\unicdbdjded}\\
((r1\_circcomb~X0~X1){\unicdcdcdhd}((r1\_partfun1~(u3\_msualg\_1~X0~X2)~(u3\_msualg\_1~\\
X1~X3)){\unicdcdcdhd}(r1\_partfun1~(u4\_msualg\_1~X0~X2)~(u4\_msualg\_1~X1~X3))))))))\end{array}
\label{hyp:egddpfdgjgchdgdgpgngcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdcdcdhd}\\
(m1\_circcmb3~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_circcmb3~X2~X0~X1){\unicdbdjdcd}((v4\_msualg\_1~\\
X2~X1){\unicdcdcdhd}(v4\_circcomb~X2~X1)))\end{array}
\label{hyp:dgdggdpfdgjgchdgdgngcgdd}
\end{equation}
\begin{theorem}\label{thm:ehcdjdpfdgjgchdgdgngcgdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_circcmb3~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_circcmb3~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m2\_circcmb3~X3~X0~X1){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_circcmb3~X4~X0~X2){\unicdbdjdcd}(v4\_circcomb~\\
(k3\_circcomb~X1~X2~X3~X4)~(k2\_circcomb~X1~X2))))))\end{array}$$
\end{theorem}
\end{document}
