\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{t11\_brouwer (TMRc9bgGJEBsjkgkEjEEJVgGARAN9uJJQSs)}
\maketitle
Let $ v3\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_brouwer : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_toprealb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r2\_abian : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k5\_brouwer : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_brouwer : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v3\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xreal\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_subset\_1~X1~k5\_numbers)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (\\
m1\_subset\_1~X3~(u1\_struct\_0~(k2\_brouwer~X1~X2~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~(u1\_struct\_0~(k2\_brouwer~X1~\\
X2~X0))~(u1\_struct\_0~(k2\_brouwer~X1~X2~X0))){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~(k2\_brouwer~X1~X2~X0))~(u1\_struct\_0~\\
(k2\_brouwer~X1~X2~X0))))))){\unicdbdjdcd}((m1\_subset\_1~X3~(u1\_struct\_0~(k7\_toprealb~\\
X1~X2~X0))){\unicdbdjdcd}((r2\_abian~(u1\_struct\_0~(k2\_brouwer~X1~X2~X0))~X3~X4){\unicdcdcdid}\\
(k4\_brouwer~X1~X2~X0~X3~X4=X3)))))))\end{array}
\label{hyp:ehjdpfcgchpgfhhhfgch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}(m1\_subset\_1~X0~k5\_numbers)){\unicdcdcdhd}(((\preoh v3\_xxreal\_0~X1){\unicdcdcdhd}(v1\_xreal\_0~\\
X1)){\unicdcdcdhd}((m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~X0))){\unicdcdcdhd}((v1\_funct\_1~\\
X3){\unicdcdcdhd}((v1\_funct\_2~X3~(u1\_struct\_0~(k2\_brouwer~X0~X2~X1))~(u1\_struct\_0~\\
(k2\_brouwer~X0~X2~X1))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k2\_brouwer~X0~X2~X1))~(u1\_struct\_0~(k2\_brouwer~X0~\\
X2~X1)))))))))){\unicdbdjdcd}((v1\_funct\_1~(k5\_brouwer~X0~X1~X2~X3)){\unicdcdcdhd}((v1\_funct\_2~\\
(k5\_brouwer~X0~X1~X2~X3)~(u1\_struct\_0~(k2\_brouwer~X0~X2~X1))~(u1\_struct\_0~\\
(k7\_toprealb~X0~X2~X1))){\unicdcdcdhd}(m1\_subset\_1~(k5\_brouwer~X0~X1~X2~X3)~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~(k2\_brouwer~X0~X2~X1))~(\\
u1\_struct\_0~(k7\_toprealb~X0~X2~X1)))))))\end{array}
\label{hyp:egehpflgfdpfcgchpgfhhhfgch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X0~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v3\_xxreal\_0~X1){\unicdcdcdhd}(v1\_xreal\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (\\
(v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(u1\_struct\_0~(k2\_brouwer~X0~X2~\\
X1))~(u1\_struct\_0~(k2\_brouwer~X0~X2~X1))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~(k2\_brouwer~X0~X2~X1))~(u1\_struct\_0~\\
(k2\_brouwer~X0~X2~X1))))))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~\\
X4~(u1\_struct\_0~(k2\_brouwer~X0~X2~X1))~(u1\_struct\_0~(k7\_toprealb~\\
X0~X2~X1))){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
(k2\_brouwer~X0~X2~X1))~(u1\_struct\_0~(k7\_toprealb~X0~X2~X1))))))){\unicdbdjdcd}\\
((X4=k5\_brouwer~X0~X1~X2~X3){\unicdbdjded}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~\\
(k2\_brouwer~X0~X2~X1))){\unicdbdjdcd}(k3\_funct\_2~(u1\_struct\_0~(k2\_brouwer~\\
X0~X2~X1))~(u1\_struct\_0~(k7\_toprealb~X0~X2~X1))~X4~X5=k4\_brouwer~\\
X0~X2~X1~X5~X3)))))))\end{array}
\label{hyp:egfdpfcgchpgfhhhfgch}
\end{equation}
\begin{theorem}\label{thm:ehbdbdpfcgchpgfhhhfgch}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v3\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xreal\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_subset\_1~X1~k5\_numbers)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (\\
m1\_subset\_1~X3~(u1\_struct\_0~(k2\_brouwer~X1~X2~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~(u1\_struct\_0~(k2\_brouwer~X1~\\
X2~X0))~(u1\_struct\_0~(k2\_brouwer~X1~X2~X0))){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~(k2\_brouwer~X1~X2~X0))~(u1\_struct\_0~\\
(k2\_brouwer~X1~X2~X0))))))){\unicdbdjdcd}((m1\_subset\_1~X3~(u1\_struct\_0~(k7\_toprealb~\\
X1~X2~X0))){\unicdbdjdcd}((r2\_abian~(u1\_struct\_0~(k2\_brouwer~X1~X2~X0))~X3~X4){\unicdcdcdid}\\
(k3\_funct\_2~(u1\_struct\_0~(k2\_brouwer~X1~X2~X0))~(u1\_struct\_0~(\\
k7\_toprealb~X1~X2~X0))~(k5\_brouwer~X1~X0~X2~X4)~X3=X3)))))))\end{array}$$
\end{theorem}
\end{document}
