\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{t17\_bcialg\_2 (TMWM47UJg9dhzMebWudxfMqghAzg3kquqEs)}
\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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k1\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_bcialg\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ 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}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k5\_numbers){\unicdbdjdcd}\\
(k1\_bcialg\_2~X0~X1~(k1\_bcialg\_1~X0~X1~(k1\_bcialg\_1~X0~X1~X2))~X3=\\
k1\_bcialg\_2~X0~X1~X2~X3))))\end{array}
\label{hyp:ehidpfcgdgjgbgmghgpfcd}
\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\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~k5\_numbers){\unicdbdjdcd}(k1\_bcialg\_2~X0~X1~(k4\_struct\_0~X0)~(k2\_nat\_1~X2~\\
np\_\_1)=X1)))\end{array}
\label{hyp:ehfdpfcgdgjgbgmghgpfcd}
\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\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}(k1\_bcialg\_2~X0~X1~X2~np\_\_1=k1\_bcialg\_1~X0~\\
X1~X2)))\end{array}
\label{hyp:ehcdpfcgdgjgbgmghgpfcd}
\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\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~k5\_numbers){\unicdbdjdcd}(k1\_bcialg\_2~X0~(k1\_bcialg\_2~X0~X1~X2~X4)~X3~X5=k1\_bcialg\_2~\\
X0~(k1\_bcialg\_2~X0~X1~X3~X5)~X2~X4))))))\end{array}
\label{hyp:ehbdbdpfcgdgjgbgmghgpfcd}
\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\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k5\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k5\_numbers){\unicdbdjdcd}(k1\_bcialg\_2~X0~(k1\_bcialg\_2~\\
X0~X1~X2~X3)~X2~X4=k1\_bcialg\_2~X0~X1~X2~(k2\_nat\_1~X3~X4))))))\end{array}
\label{hyp:ehbdadpfcgdgjgbgmghgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\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 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\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}((m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X3~k5\_numbers)))){\unicdbdjdcd}\\
(m1\_subset\_1~(k1\_bcialg\_2~X0~X1~X2~X3)~(u1\_struct\_0~X0))\end{array}
\label{hyp:egehpflgbdpfcgdgjgbgmghgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_bcialg\_1~X0)){\unicdbdjdcd}((v5\_bcialg\_1~\\
X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k1\_bcialg\_1~\\
X0~X1~X1=k4\_struct\_0~X0)))\end{array}
\label{hyp:egfdpfcgdgjgbgmghgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdhdpfcgdgjgbgmghgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_bcialg\_1~X0){\unicdcdcdhd}((v4\_bcialg\_1~\\
X0){\unicdcdcdhd}((v5\_bcialg\_1~X0){\unicdcdcdhd}((v7\_bcialg\_1~X0){\unicdcdcdhd}(l2\_bcialg\_1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k5\_numbers){\unicdbdjdcd}\\
((k1\_bcialg\_1~X0~X1~X2=X1){\unicdbdjdcd}(k1\_bcialg\_2~X0~X1~X2~X3=X1)))))\end{array}$$
\end{theorem}
\end{document}
