\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{l60\_turing\_1 (TMGTBipbQPfDrjPEfQPv7F4Af4tGkzpDr3L)}
\maketitle
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_4 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u2\_turing\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_turing\_1 : {\iota}$ be given.
Let $ k16\_turing\_1 : {\iota}$ be given.
Let $ v1\_turing\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_turing\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_turing\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_turing\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k8\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k9\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ u3\_turing\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_turing\_1 : {\iota}$ be given.
Let $ u4\_turing\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u5\_turing\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_turing\_1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}((r1\_xxreal\_0~\\
X0~np\_\_4){\unicdbdjdcd}(m1\_subset\_1~X0~(u2\_turing\_1~k16\_turing\_1)))\end{array}
\label{hyp:mgfdcdpfehfhchjgoghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{({{v1\_turing\_1}~{k18\_turing\_1}})}{\unicdcdcdhd}{({{l1\_turing\_1}~{k18\_turing\_1}})}}\label{hyp:egehpflgbdidpfehfhchjgoghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{({{v1\_turing\_1}~{k16\_turing\_1}})}{\unicdcdcdhd}{({{l1\_turing\_1}~{k16\_turing\_1}})}}\label{hyp:egehpflgbdgdpfehfhchjgoghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_turing\_1~X0){\unicdcdcdhd}(l1\_turing\_1~X0)){\unicdbdjdcd}((X0=k18\_turing\_1){\unicdbdjded}\\
((u1\_turing\_1~X0=k7\_domain\_1~k5\_numbers~k6\_numbers~np\_\_1){\unicdcdcdhd}(\\
(u2\_turing\_1~X0=k3\_turing\_1~np\_\_4){\unicdcdcdhd}((r1\_funct\_2~(k2\_zfmisc\_1~\\
(u2\_turing\_1~X0)~(u1\_turing\_1~X0))~(k3\_zfmisc\_1~(u2\_turing\_1~\\
X0)~(u1\_turing\_1~X0)~(k8\_domain\_1~k1\_numbers~(k1\_real\_1~np\_\_1)~\\
k6\_numbers~np\_\_1))~(k8\_mcart\_1~k5\_numbers~k5\_numbers~(k3\_turing\_1~\\
np\_\_4)~(k7\_domain\_1~k5\_numbers~k6\_numbers~np\_\_1))~(k9\_mcart\_1~\\
k5\_numbers~k5\_numbers~k1\_numbers~(k3\_turing\_1~np\_\_4)~(k7\_domain\_1~\\
k5\_numbers~k6\_numbers~np\_\_1)~(k8\_domain\_1~k1\_numbers~(k1\_real\_1~\\
np\_\_1)~k6\_numbers~np\_\_1))~(u3\_turing\_1~X0)~k17\_turing\_1){\unicdcdcdhd}((u4\_turing\_1~\\
X0=k6\_numbers){\unicdcdcdhd}(u5\_turing\_1~X0=np\_\_4))))))\end{array}
\label{hyp:egbdjdpfehfhchjgoghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_turing\_1~X0){\unicdcdcdhd}(l1\_turing\_1~X0)){\unicdbdjdcd}((X0=k16\_turing\_1){\unicdbdjded}\\
((u1\_turing\_1~X0=k7\_domain\_1~k5\_numbers~k6\_numbers~np\_\_1){\unicdcdcdhd}(\\
(u2\_turing\_1~X0=k3\_turing\_1~np\_\_4){\unicdcdcdhd}((r1\_funct\_2~(k2\_zfmisc\_1~\\
(u2\_turing\_1~X0)~(u1\_turing\_1~X0))~(k3\_zfmisc\_1~(u2\_turing\_1~\\
X0)~(u1\_turing\_1~X0)~(k8\_domain\_1~k1\_numbers~(k1\_real\_1~np\_\_1)~\\
k6\_numbers~np\_\_1))~(k8\_mcart\_1~k5\_numbers~k5\_numbers~(k3\_turing\_1~\\
np\_\_4)~(k7\_domain\_1~k5\_numbers~k6\_numbers~np\_\_1))~(k9\_mcart\_1~\\
k5\_numbers~k5\_numbers~k1\_numbers~(k3\_turing\_1~np\_\_4)~(k7\_domain\_1~\\
k5\_numbers~k6\_numbers~np\_\_1)~(k8\_domain\_1~k1\_numbers~(k1\_real\_1~\\
np\_\_1)~k6\_numbers~np\_\_1))~(u3\_turing\_1~X0)~k15\_turing\_1){\unicdcdcdhd}((u4\_turing\_1~\\
X0=k6\_numbers){\unicdcdcdhd}(u5\_turing\_1~X0=np\_\_4))))))\end{array}
\label{hyp:egbdhdpfehfhchjgoghgpfbd}
\end{equation}
\begin{theorem}\label{thm:mggdadpfehfhchjgoghgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}((r1\_xxreal\_0~\\
X0~np\_\_4){\unicdbdjdcd}(m1\_subset\_1~X0~(u2\_turing\_1~k18\_turing\_1)))\end{array}$$
\end{theorem}
\end{document}
