\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{t41\_mycielsk (TMZMaJZEZWV7s4Jdv1uNasgho25EFC6d98Y)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_mycielsk : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_orders\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_mycielsk : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k3\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(X5 \in k2\_xboole\_0~(k2\_xboole\_0~(k2\_xboole\_0~(k2\_xboole\_0~X0~X1)~\\
X2)~X3)~X4){\unicdbdjded}(\preoh (\preoh X5 \in X0){\unicdcdcdhd}((\preoh X5 \in X1){\unicdcdcdhd}((\preoh X5 \in X2){\unicdcdcdhd}((\preoh X5 \in X3){\unicdcdcdhd}(\preoh X5 \in \\
X4)))))\end{array}
\label{hyp:ehedpfngjhdgjgfgmgdhlg}
\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}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(m1\_mycielsk~X1~X0)){\unicdbdjdcd}\\
(m1\_mycielsk~(k6\_mycielsk~X0~X1)~(k2\_xcmplx\_0~(k3\_xcmplx\_0~np\_\_2~\\
X0)~np\_\_1))\end{array}
\label{hyp:egehpflggdpfngjhdgjgfgmgdhlg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_mycielsk~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_mycielsk~X2~(k2\_xcmplx\_0~(k3\_xcmplx\_0~np\_\_2~X0)~\\
np\_\_1)){\unicdbdjdcd}((X2=k6\_mycielsk~X0~X1){\unicdbdjded}(u1\_orders\_2~X2=k2\_xboole\_0~\\
(k2\_xboole\_0~(k2\_xboole\_0~(k2\_xboole\_0~(u1\_orders\_2~X1)~(ReplSep2~\\
(toset~({\uniddcgcg} X3 : \iota .  m1\_subset\_1~X3~k5\_numbers))~({\uniddcgcg} X3 : \iota .  \\
toset~({\uniddcgcg} X4 : \iota .  m1\_subset\_1~X4~k5\_numbers))~({\uniddcgcg} X3 : \iota .  {\uniddcgcg} X4 : \\
\iota .  k4\_tarski~X3~X4 \in u1\_orders\_2~X1)~({\uniddcgcg} X3 : \iota .  {\uniddcgcg} X4 : \iota .  \\
k4\_tarski~X3~(k2\_xcmplx\_0~X4~X0))))~(ReplSep2~(toset~({\uniddcgcg} X3 : \iota .  \\
m1\_subset\_1~X3~k5\_numbers))~({\uniddcgcg} X3 : \iota .  toset~({\uniddcgcg} X4 : \iota .  m1\_subset\_1~\\
X4~k5\_numbers))~({\uniddcgcg} X3 : \iota .  {\uniddcgcg} X4 : \iota .  k4\_tarski~X3~X4 \in u1\_orders\_2~\\
X1)~({\uniddcgcg} X3 : \iota .  {\uniddcgcg} X4 : \iota .  k4\_tarski~(k2\_xcmplx\_0~X3~X0)~X4)))~\\
(k2\_zfmisc\_1~(k1\_tarski~(k3\_xcmplx\_0~np\_\_2~X0))~(k6\_subset\_1~\\
(k3\_xcmplx\_0~np\_\_2~X0)~X0)))~(k2\_zfmisc\_1~(k6\_subset\_1~(k3\_xcmplx\_0~\\
np\_\_2~X0)~X0)~(k1\_tarski~(k3\_xcmplx\_0~np\_\_2~X0)))))))\end{array}
\label{hyp:egjdpfngjhdgjgfgmgdhlg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjded}{({{X0} \in {k4\_ordinal1}})}}}\label{hyp:egbdcdpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehedbdpfngjhdgjgfgmgdhlg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_mycielsk~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}(\\
(k4\_tarski~X2~X3 \in u1\_orders\_2~X1){\unicdbdjdcd}((k4\_tarski~X2~(k2\_xcmplx\_0~\\
X3~X0) \in u1\_orders\_2~(k6\_mycielsk~X0~X1)){\unicdcdcdhd}(k4\_tarski~(k2\_xcmplx\_0~\\
X2~X0)~X3 \in u1\_orders\_2~(k6\_mycielsk~X0~X1)))))))\end{array}$$
\end{theorem}
\end{document}
