\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=}
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\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t20\_bcialg\_4 (TMQcDjS475PJCpSwaCP4cU4AYbuxxzJu65c)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_bcialg\_4 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_bcialg\_4 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_bcialg\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_bcialg\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k1\_bcialg\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k1\_xboole\_0}}~{k4\_ordinal1}}\label{hyp:ehbdpfogfhngfgchbgmgdh}
\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 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_bcialg\_1~X0){\unicdcdcdhd}((v4\_bcialg\_1~\\
X0){\unicdcdcdhd}((v5\_bcialg\_1~X0){\unicdcdcdhd}((v7\_bcialg\_1~X0){\unicdcdcdhd}((v2\_bcialg\_4~X0){\unicdcdcdhd}\\
(l1\_bcialg\_4~X0))))))){\unicdbdjdcd}((v1\_funct\_1~(k5\_bcialg\_4~X0)){\unicdcdcdhd}((v1\_funct\_2~\\
(k5\_bcialg\_4~X0)~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~k5\_numbers)~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~(k5\_bcialg\_4~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~k5\_numbers)~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpflgfdpfcgdgjgbgmghgpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_bcialg\_1~X0){\unicdcdcdhd}((v4\_bcialg\_1~\\
X0){\unicdcdcdhd}((v5\_bcialg\_1~X0){\unicdcdcdhd}((v7\_bcialg\_1~X0){\unicdcdcdhd}((v2\_bcialg\_4~X0){\unicdcdcdhd}\\
(l1\_bcialg\_4~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}(k6\_bcialg\_4~X0~\\
X1~X2=k2\_binop\_1~(u1\_struct\_0~X0)~k5\_numbers~(u1\_struct\_0~X0)~\\
(k5\_bcialg\_4~X0)~X1~X2)))\end{array}
\label{hyp:eghdpfcgdgjgbgmghgpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_bcialg\_1~X0){\unicdcdcdhd}((v4\_bcialg\_1~\\
X0){\unicdcdcdhd}((v5\_bcialg\_1~X0){\unicdcdcdhd}((v7\_bcialg\_1~X0){\unicdcdcdhd}((v2\_bcialg\_4~X0){\unicdcdcdhd}\\
(l1\_bcialg\_4~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~k5\_numbers)~(u1\_struct\_0~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~k5\_numbers)~(u1\_struct\_0~X0)))))){\unicdbdjdcd}((X1=k5\_bcialg\_4~X0){\unicdbdjded}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((k2\_binop\_1~(\\
u1\_struct\_0~X0)~k5\_numbers~(u1\_struct\_0~X0)~X1~X2~k6\_numbers=k4\_struct\_0~\\
X0){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k5\_numbers){\unicdbdjdcd}(k2\_binop\_1~(u1\_struct\_0~\\
X0)~k5\_numbers~(u1\_struct\_0~X0)~X1~X2~(k2\_nat\_1~X3~np\_\_1)=k1\_bcialg\_4~\\
X0~(k2\_binop\_1~(u1\_struct\_0~X0)~k5\_numbers~(u1\_struct\_0~X0)~X1~\\
X2~X3)~X2))))))\end{array}
\label{hyp:eggdpfcgdgjgbgmghgpfed}
\end{equation}
\begin{theorem}\label{thm:ehcdadpfcgdgjgbgmghgpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_bcialg\_1~X0){\unicdcdcdhd}((v4\_bcialg\_1~\\
X0){\unicdcdcdhd}((v5\_bcialg\_1~X0){\unicdcdcdhd}((v7\_bcialg\_1~X0){\unicdcdcdhd}((v2\_bcialg\_4~X0){\unicdcdcdhd}\\
(l1\_bcialg\_4~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(k6\_bcialg\_4~X0~X1~k6\_numbers=k4\_struct\_0~X0))\end{array}$$
\end{theorem}
\end{document}
