\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{t49\_bcialg\_2 (TMVcPq92y31MoR11sUnTu5ETGmK382D8UGm)}
\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 $ l2\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m4\_bcialg\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_bcialg\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m3\_bcialg\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m5\_bcialg\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v12\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m2\_bcialg\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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}(l2\_bcialg\_1~X0)))))){\unicdbdjdcd}\\
((v12\_bcialg\_1~(u1\_struct\_0~X0)~X0){\unicdcdcdhd}(m2\_bcialg\_1~(u1\_struct\_0~\\
X0)~X0))\end{array}
\label{hyp:ehededpfcgdgjgbgmghgpfbd}
\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}(l2\_bcialg\_1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m2\_bcialg\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_bcialg\_1~X2~X0){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m5\_bcialg\_2~X3~X0~X1){\unicdbdjdcd}({\unicdcdadad} X4 .  (m5\_bcialg\_2~X4~\\
X0~X2){\unicdbdjdcd}((k6\_eqrel\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X3~(k4\_struct\_0~\\
X0)=k6\_eqrel\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X4~(k4\_struct\_0~\\
X0)){\unicdbdjdcd}(X3=X4))))))\end{array}
\label{hyp:ehedbdpfcgdgjgbgmghgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~X1)){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddpfdhfhcgdhfgeh}
\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}(l2\_bcialg\_1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m2\_bcialg\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m4\_bcialg\_2~X2~X0~\\
X1){\unicdbdjdcd}((v12\_bcialg\_1~X1~X0){\unicdbdjded}(X1=k6\_eqrel\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0)~X2~(k4\_struct\_0~X0)))))\end{array}
\label{hyp:ehddjdpfcgdgjgbgmghgpfcd}
\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}(l2\_bcialg\_1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m2\_bcialg\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m4\_bcialg\_2~X2~X0~\\
X1){\unicdbdjdcd}(r1\_tarski~(k6\_eqrel\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~\\
X2~(k4\_struct\_0~X0))~X1)))\end{array}
\label{hyp:ehddidpfcgdgjgbgmghgpfcd}
\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}(l2\_bcialg\_1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_partfun1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}((v3\_relat\_2~\\
X1){\unicdcdcdhd}((v8\_relat\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0))))))){\unicdbdjdcd}((m1\_bcialg\_2~X1~X0){\unicdbdjded}\\
((m3\_bcialg\_2~X1~X0){\unicdcdcdhd}(m2\_bcialg\_2~X1~X0))))\end{array}
\label{hyp:ehddgdpfcgdgjgbgmghgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\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}(l2\_bcialg\_1~\\
X0)))))){\unicdcdcdhd}(m2\_bcialg\_1~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m5\_bcialg\_2~X2~X0~\\
X1){\unicdbdjded}(m4\_bcialg\_2~X2~X0~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngfdpfcgdgjgbgmghgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\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}(l2\_bcialg\_1~\\
X0)))))){\unicdcdcdhd}(m2\_bcialg\_1~X1~X0)){\unicdbdjdcd}({\unicdcdaddd} X2 .  m5\_bcialg\_2~X2~X0~X1)\end{array}
\label{hyp:fgihjgdhehfgogdgfgpfngfdpfcgdgjgbgmghgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\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}(l2\_bcialg\_1~\\
X0)))))){\unicdcdcdhd}(m2\_bcialg\_1~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m5\_bcialg\_2~X2~X0~\\
X1){\unicdbdjdcd}(m1\_bcialg\_2~X2~X0))\end{array}
\label{hyp:egehpfngfdpfcgdgjgbgmghgpfcd}
\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}(l2\_bcialg\_1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m2\_bcialg\_1~X1~X0){\unicdbdjdcd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))))\end{array}
\label{hyp:egehpfngcdpfcgdgjgbgmghgpfbd}
\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}(l2\_bcialg\_1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_bcialg\_2~X1~X0){\unicdbdjdcd}((v1\_partfun1~X1~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((v3\_relat\_2~X1){\unicdcdcdhd}((v8\_relat\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))))))))\end{array}
\label{hyp:egehpfngbdpfcgdgjgbgmghgpfcd}
\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:ehedjdpfcgdgjgbgmghgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_bcialg\_1~X0){\unicdcdcdhd}((v4\_bcialg\_1~\\
X0){\unicdcdcdhd}((v5\_bcialg\_1~X0){\unicdcdcdhd}((v7\_bcialg\_1~X0){\unicdcdcdhd}(l2\_bcialg\_1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m2\_bcialg\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m4\_bcialg\_2~X2~X0~\\
X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_bcialg\_2~X3~X0){\unicdbdjdcd}(({\unicdcdadad} X4 .  (m3\_bcialg\_2~\\
X4~X0){\unicdbdjdcd}(m5\_bcialg\_2~X4~X0~X1)){\unicdbdjdcd}(X3=X2)))))\end{array}$$
\end{theorem}
\end{document}
