\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\_irrat\_1 (TML12c71HyfnBGrriQcDsxL9dxoXB4LbdsS)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ k5\_numbers : {\iota}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\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 $ v2\_comseq\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_seq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~\\
k5\_numbers~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k5\_numbers~k1\_numbers))))){\unicdbdjdcd}(\preoh (v2\_comseq\_2~X2){\unicdcdcdhd}((k2\_seq\_2~X2=\\
X0){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X1~k6\_numbers){\unicdcdcdhd}({\unicdcdadad} X3 .  (m2\_subset\_1~\\
X3~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdaddd} X4 .  (m2\_subset\_1~X4~k1\_numbers~\\
k5\_numbers){\unicdcdcdhd}((r1\_xxreal\_0~X3~X4){\unicdcdcdhd}(\preoh (\preoh r1\_xxreal\_0~(k1\_seq\_1~\\
X2~X4)~(k9\_real\_1~X0~X1)){\unicdcdcdhd}(\preoh r1\_xxreal\_0~(k7\_real\_1~X0~X1)~(k1\_seq\_1~\\
X2~X4)))))))))))\end{array}
\label{hyp:ehhdpfmgjgngggfhogdgdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k1\_numbers){\unicdcdcdhd}(v1\_xreal\_0~\\
X1)){\unicdbdjdcd}(k9\_real\_1~X0~X1=k6\_xcmplx\_0~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjded}{({{X0} \in {k1\_numbers}})}}}\label{hyp:egbdpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehcdfdpfjgchchbgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~k5\_numbers~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k5\_numbers~k1\_numbers))))){\unicdbdjdcd}(((v2\_comseq\_2~X1){\unicdcdcdhd}(k2\_seq\_2~X1=\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_xreal\_0~X2){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X2~k6\_numbers){\unicdcdcdhd}\\
({\unicdcdadad} X3 .  (m2\_subset\_1~X3~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdaddd} X4 .  \\
(m2\_subset\_1~X4~k1\_numbers~k5\_numbers){\unicdcdcdhd}((r1\_xxreal\_0~X3~X4){\unicdcdcdhd}\\
(r1\_xxreal\_0~(k1\_seq\_1~X1~X4)~(k6\_xcmplx\_0~X0~X2)))))))))\end{array}$$
\end{theorem}
\end{document}
