\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{t7\_chord (TMTkY544PCrCx8AdnZP4ZcRKTFs4i3P3HDf)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_abian : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_4 : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_int\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}(\preoh (r1\_xxreal\_0~X0~np\_\_4){\unicdcdcdhd}((X0{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}\\
((X0{\unicdcdgdad}np\_\_1){\unicdcdcdhd}((X0{\unicdcdgdad}np\_\_2){\unicdcdcdhd}((X0{\unicdcdgdad}np\_\_3){\unicdcdcdhd}(X0{\unicdcdgdad}np\_\_4))))))\end{array}
\label{hyp:ehcdidpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{{{k2\_xcmplx\_0}~{X0}}~{k6\_numbers}}={X0}})}}}\label{hyp:ehbdpfbgchjgehigng}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_abian}~{np\_\_2}}\label{hyp:mgedpfmgbgehehjgdgfgid}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_abian}~{np\_\_4}}\label{hyp:mgddpfahpgmgjhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_int\_1~X0){\unicdbdjdcd}((v1\_xcmplx\_0~(k4\_xcmplx\_0~X0)){\unicdcdcdhd}(v1\_int\_1~\\
(k4\_xcmplx\_0~X0)))\end{array}
\label{hyp:ggdgddpfjgogehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_int\_1~X0){\unicdcdcdhd}(\preoh v1\_abian~X0)){\unicdbdjdcd}((v1\_xcmplx\_0~(k4\_xcmplx\_0~\\
X0)){\unicdcdcdhd}(\preoh v1\_abian~(k4\_xcmplx\_0~X0)))\end{array}
\label{hyp:ggdgbdpfggjgcgpfogfhngcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_int\_1~X0){\unicdcdcdhd}(\preoh v1\_abian~X0)){\unicdcdcdhd}((v1\_int\_1~\\
X1){\unicdcdcdhd}(\preoh v1\_abian~X1))){\unicdbdjdcd}(v1\_abian~(k2\_xcmplx\_0~X0~X1))\end{array}
\label{hyp:ggdgbdcdpfbgcgjgbgog}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v1\_int\_1}~{X0}})}}}\label{hyp:dgdgcdpfjgogehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehhdpfdgigpgcheg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(\preoh v1\_abian~X0)){\unicdbdjdcd}(\preoh (r1\_xxreal\_0~\\
X0~np\_\_4){\unicdcdcdhd}((X0{\unicdcdgdad}np\_\_1){\unicdcdcdhd}(X0{\unicdcdgdad}np\_\_3)))\end{array}$$
\end{theorem}
\end{document}
