\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdbdjded{\Leftrightarrow}
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\begin{document}
\title{t6\_turing\_1 (TMQm5fpJiy3Eaj1ZjUf7ftJ9w2EcJYbthcP)}
\maketitle
Let $ l1\_turing\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u2\_turing\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_numbers : {\iota}$ be given.
Let $ k9\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_turing\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ u5\_turing\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_turing\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_xtuple\_0 : {{\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\_numbers : {\iota}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k8\_turing\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_turing\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_turing\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_turing\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_turing\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k3\_zfmisc\_1~\\
(u2\_turing\_1~X0)~k4\_numbers~(k9\_funct\_2~k4\_numbers~(u1\_turing\_1~\\
X0)))){\unicdbdjdcd}(((k1\_mcart\_1~(u2\_turing\_1~X0)~k4\_numbers~(k9\_funct\_2~\\
k4\_numbers~(u1\_turing\_1~X0))~X1{\unicdcdgdad}u5\_turing\_1~X0){\unicdbdjdcd}(k9\_turing\_1~\\
X0~X1=k3\_xtuple\_0~(k1\_mcart\_1~(u2\_turing\_1~X0)~(u1\_turing\_1~X0)~\\
(k8\_domain\_1~k1\_numbers~(k1\_real\_1~np\_\_1)~k6\_numbers~np\_\_1)~(\\
k8\_turing\_1~X0~X1))~(k2\_xcmplx\_0~(k7\_turing\_1~X0~X1)~(k6\_turing\_1~\\
X0~(k8\_turing\_1~X0~X1)))~(k5\_turing\_1~X0~(k3\_mcart\_1~(u2\_turing\_1~\\
X0)~k4\_numbers~(k9\_funct\_2~k4\_numbers~(u1\_turing\_1~X0))~X1)~(k7\_turing\_1~\\
X0~X1)~(k2\_mcart\_1~(u2\_turing\_1~X0)~(u1\_turing\_1~X0)~(k8\_domain\_1~\\
k1\_numbers~(k1\_real\_1~np\_\_1)~k6\_numbers~np\_\_1)~(k8\_turing\_1~X0~\\
X1))))){\unicdcdcdhd}((k1\_mcart\_1~(u2\_turing\_1~X0)~k4\_numbers~(k9\_funct\_2~\\
k4\_numbers~(u1\_turing\_1~X0))~X1=u5\_turing\_1~X0){\unicdbdjdcd}(k9\_turing\_1~\\
X0~X1=X1))))\end{array}
\label{hyp:eggdpfehfhchjgoghgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehgdpfehfhchjgoghgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (l1\_turing\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k3\_zfmisc\_1~\\
(u2\_turing\_1~X0)~k4\_numbers~(k9\_funct\_2~k4\_numbers~(u1\_turing\_1~\\
X0)))){\unicdbdjdcd}((k1\_mcart\_1~(u2\_turing\_1~X0)~k4\_numbers~(k9\_funct\_2~\\
k4\_numbers~(u1\_turing\_1~X0))~X1=u5\_turing\_1~X0){\unicdbdjdcd}(X1=k9\_turing\_1~\\
X0~X1)))\end{array}$$
\end{theorem}
\end{document}
