\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{t20\_catalan1 (TMZPCNoVRTyVnrcm8CaC419oWTPFRf4q9uW)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_catalan1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k1\_newton : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}(\preoh \\
(r1\_xxreal\_0~X0~(k1\_nat\_1~X1~np\_\_1)){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X0~X1){\unicdcdcdhd}(X0{\unicdcdgdad}\\
k1\_nat\_1~X1~np\_\_1))))\end{array}
\label{hyp:ehidpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((\\
\preoh (\preoh (X0=k6\_numbers){\unicdcdcdhd}(X1{\unicdcdgdad}k6\_numbers)){\unicdcdcdhd}(k1\_newton~X0~X1=k6\_numbers)){\unicdcdcdhd}\\
(\preoh (k1\_newton~X0~X1{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}((X0=k6\_numbers){\unicdcdcdhd}(X1{\unicdcdgdad}k6\_numbers)))))\end{array}
\label{hyp:ehidhdpfogfghhehpgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}(\preoh (X0{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}({\unicdcdadad} X1 .  \\
(v7\_ordinal1~X1){\unicdbdjdcd}(X0{\unicdcdgdad}k1\_nat\_1~X1~np\_\_1)))\end{array}
\label{hyp:ehgdpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{{{k1\_newton}~{X0}}~{k6\_numbers}}={np\_\_1}})}}}\label{hyp:ehedpfogfghhehpgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}(\preoh (k6\_numbers{\unicdcdgdad}X0){\unicdcdcdhd}(r1\_xxreal\_0~\\
X0~k6\_numbers))\end{array}
\label{hyp:ehddpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}(\preoh (r1\_xxreal\_0~X0~np\_\_1){\unicdcdcdhd}((X0{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}\\
(X0{\unicdcdgdad}np\_\_1)))\end{array}
\label{hyp:ehcdfdpfogbgehpfbd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((\\
\preoh r1\_xxreal\_0~(k2\_xcmplx\_0~X0~X1)~X0){\unicdbdjded}(r1\_xxreal\_0~np\_\_1~X1)))\end{array}
\label{hyp:ehbdjdpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}(r1\_xxreal\_0~(k1\_catalan1~X0)~(k1\_catalan1~\\
(k1\_nat\_1~X0~np\_\_1)))\end{array}
\label{hyp:ehbdgdpfdgbgehbgmgbgogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X0~np\_\_1){\unicdcdcdhd}(r1\_xxreal\_0~\\
(k1\_catalan1~(k1\_nat\_1~X0~np\_\_1))~(k1\_catalan1~X0)))\end{array}
\label{hyp:ehbdfdpfdgbgehbgmgbgogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((\preoh r1\_xxreal\_0~np\_\_1~X0){\unicdbdjdcd}(X0=k6\_numbers))\end{array}
\label{hyp:ehbdedpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{{k1\_catalan1}~{np\_\_1}}={np\_\_1}}\label{hyp:ehbdbdpfdgbgehbgmgbgogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}(\\
v7\_ordinal1~(k1\_newton~X0~X1))\end{array}
\label{hyp:ggdgedpfogfghhehpgog}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{({{k1\_catalan1}~{X0}})}})}}}\label{hyp:ggdgbdpfdgbgehbgmgbgogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}(m1\_subset\_1~(k1\_catalan1~X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdpfdgbgehbgmgbgogbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgbdpfihdgngahmgihpfad}
\end{equation}
\begin{theorem}\label{thm:ehcdadpfdgbgehbgmgbgogbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X0~k6\_numbers){\unicdcdcdhd}\\
(r1\_xxreal\_0~(k1\_catalan1~X0)~k6\_numbers))\end{array}$$
\end{theorem}
\end{document}
