\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{t25\_circcomb (TMajRvWdHWvXuWyRdheDN7DnomqgYdkyn54)}
\maketitle
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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l5\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u4\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u2\_msualg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v2\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v2\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k4\_card\_3~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(k4\_card\_3~X1)){\unicdbdjdcd}(k1\_funct\_4~X2~X3 \in k4\_card\_3~(k1\_funct\_4~X0~\\
X1)))))\end{array}
\label{hyp:ehjdhdpfdgbgchegpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_struct\_0~X0){\unicdcdcdhd}((v4\_msualg\_1~X1~X0){\unicdcdcdhd}\\
(l2\_msualg\_1~X1~X0))){\unicdbdjdcd}((v1\_relat\_1~(u3\_msualg\_1~X0~X1)){\unicdcdcdhd}((v2\_relat\_1~\\
(u3\_msualg\_1~X0~X1)){\unicdcdcdhd}((v4\_relat\_1~(u3\_msualg\_1~X0~X1)~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((v1\_funct\_1~(u3\_msualg\_1~X0~X1)){\unicdcdcdhd}(v1\_partfun1~(u3\_msualg\_1~\\
X0~X1)~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:ggdgbdpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_struct\_0~X0){\unicdcdcdhd}(l2\_msualg\_1~X1~X0)){\unicdbdjdcd}\\
((v1\_relat\_1~(u3\_msualg\_1~X0~X1)){\unicdcdcdhd}((v4\_relat\_1~(u3\_msualg\_1~\\
X0~X1)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_funct\_1~(u3\_msualg\_1~X0~X1)){\unicdcdcdhd}(v1\_partfun1~\\
(u3\_msualg\_1~X0~X1)~(u1\_struct\_0~X0)))))\end{array}
\label{hyp:egehpffhddpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l5\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgfdpfdhehchfhdgehpfad}
\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 .  \\
(l3\_msualg\_1~X1~X0){\unicdbdjdcd}(l2\_msualg\_1~X1~X0))\end{array}
\label{hyp:egehpfmgddpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_msualg\_1}~{X0}})}{\unicdbdjdcd}{({{l5\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)){\unicdcdcdhd}\\
(((v4\_msualg\_1~X2~X0){\unicdcdcdhd}(l3\_msualg\_1~X2~X0)){\unicdcdcdhd}((v4\_msualg\_1~X3~X1){\unicdcdcdhd}\\
(l3\_msualg\_1~X3~X1))))){\unicdbdjdcd}((v3\_msualg\_1~(k3\_circcomb~X0~X1~X2~X3)~\\
(k2\_circcomb~X0~X1)){\unicdcdcdhd}((v4\_msualg\_1~(k3\_circcomb~X0~X1~X2~X3)~(k2\_circcomb~\\
X0~X1)){\unicdcdcdhd}(l3\_msualg\_1~(k3\_circcomb~X0~X1~X2~X3)~(k2\_circcomb~X0~X1))))\end{array}
\label{hyp:egehpflgddpfdgjgchdgdgpgngcg}
\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 .  ((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}((r1\_partfun1~(u3\_msualg\_1~X0~X2)~(u3\_msualg\_1~\\
X1~X3)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v3\_msualg\_1~X4~(k2\_circcomb~X0~X1)){\unicdcdcdhd}((v4\_msualg\_1~\\
X4~(k2\_circcomb~X0~X1)){\unicdcdcdhd}(l3\_msualg\_1~X4~(k2\_circcomb~X0~X1)))){\unicdbdjdcd}\\
((X4=k3\_circcomb~X0~X1~X2~X3){\unicdbdjded}((u3\_msualg\_1~(k2\_circcomb~X0~X1)~\\
X4=k1\_funct\_4~(u3\_msualg\_1~X0~X2)~(u3\_msualg\_1~X1~X3)){\unicdcdcdhd}(u4\_msualg\_1~\\
(k2\_circcomb~X0~X1)~X4=k1\_circcomb~(u4\_struct\_0~X0)~(k3\_relat\_1~\\
(u1\_msualg\_1~X0)~(k6\_finseq\_2~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~\\
X2)))~(k3\_relat\_1~(u2\_msualg\_1~X0)~(u3\_msualg\_1~X0~X2))~(u4\_struct\_0~\\
X1)~(k3\_relat\_1~(u1\_msualg\_1~X1)~(k6\_finseq\_2~(u1\_struct\_0~X1)~\\
(u3\_msualg\_1~X1~X3)))~(k3\_relat\_1~(u2\_msualg\_1~X1)~(u3\_msualg\_1~\\
X1~X3))~(u4\_msualg\_1~X0~X2)~(u4\_msualg\_1~X1~X3)))))))))\end{array}
\label{hyp:egedpfdgjgchdgdgpgngcg}
\end{equation}
\begin{theorem}\label{thm:ehcdfdpfdgjgchdgdgpgngcg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v4\_msualg\_1~\\
X2~X0){\unicdcdcdhd}(l3\_msualg\_1~X2~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k4\_card\_3~\\
(u3\_msualg\_1~X0~X2))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v4\_msualg\_1~X4~X1){\unicdcdcdhd}(l3\_msualg\_1~\\
X4~X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(k4\_card\_3~(u3\_msualg\_1~X1~\\
X4))){\unicdbdjdcd}((r1\_partfun1~(u3\_msualg\_1~X0~X2)~(u3\_msualg\_1~X1~X4)){\unicdbdjdcd}\\
(k1\_funct\_4~X3~X5 \in k4\_card\_3~(u3\_msualg\_1~(k2\_circcomb~X0~X1)~(\\
k3\_circcomb~X0~X1~X2~X4)))))))))\end{array}$$
\end{theorem}
\end{document}
