\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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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t19\_turing\_1 (TMG9KRppUbfNNBAyDU9ZcgsrHJ2CaXJ8CWE)}
\maketitle
Let $ l1\_turing\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k4\_numbers : {\iota}$ be given.
Let $ u1\_turing\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
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 $ r2\_turing\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_finseq\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ np\_\_4 : {\iota}$ be given.
Let $ v1\_int\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ r1\_turing\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_turing\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_funct\_2~X1~k4\_numbers~\\
(u1\_turing\_1~X0)~(k9\_funct\_2~k4\_numbers~(u1\_turing\_1~X0))){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m2\_subset\_1~X3~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_subset\_1~\\
X4~k1\_numbers~k5\_numbers){\unicdbdjdcd}((r2\_turing\_1~(k3\_finseq\_4~k5\_numbers~\\
X2~X3~X4)~X0~X1){\unicdbdjdcd}((r1\_turing\_1~X0~X1~X2~(k2\_nat\_1~(k2\_nat\_1~X2~X3)~\\
np\_\_2)){\unicdcdcdhd}(r1\_turing\_1~X0~X1~(k2\_nat\_1~(k2\_nat\_1~X2~X3)~np\_\_2)~(k2\_nat\_1~\\
(k2\_nat\_1~(k2\_nat\_1~X2~X3)~X4)~np\_\_4))))))))\end{array}
\label{hyp:ehbdidpfehfhchjgoghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_4){\unicdcdcdhd}(m2\_subset\_1~np\_\_4~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_4~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_4~k1\_numbers))\end{array}
\label{hyp:dhahdgedpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_2){\unicdcdcdhd}(m2\_subset\_1~np\_\_2~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_2~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_2~k1\_numbers))\end{array}
\label{hyp:dhahdgcdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k5\_numbers}}~{({{k1\_zfmisc\_1}~{k1\_numbers}})}}\label{hyp:egehpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k5\_numbers){\unicdcdcdhd}(v7\_ordinal1~\\
X1)){\unicdbdjdcd}(m2\_subset\_1~(k2\_nat\_1~X0~X1)~k1\_numbers~k5\_numbers)\end{array}
\label{hyp:egehpflgcdpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_turing\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_funct\_2~X1~k4\_numbers~\\
(u1\_turing\_1~X0)~(k9\_funct\_2~k4\_numbers~(u1\_turing\_1~X0))){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (v1\_int\_1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_int\_1~X3){\unicdbdjdcd}((r1\_turing\_1~\\
X0~X1~X2~X3){\unicdbdjded}((k1\_funct\_1~X1~X2=k6\_numbers){\unicdcdcdhd}((k1\_funct\_1~X1~X3=\\
k6\_numbers){\unicdcdcdhd}({\unicdcdadad} X4 .  (v1\_int\_1~X4){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X4~X2){\unicdcdcdhd}\\
((\preoh r1\_xxreal\_0~X3~X4){\unicdcdcdhd}(k1\_funct\_1~X1~X4{\unicdcdgdad}np\_\_1))))))))))\end{array}
\label{hyp:egbdcdpfehfhchjgoghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k5\_numbers){\unicdcdcdhd}(v7\_ordinal1~\\
X1)){\unicdbdjdcd}(k2\_nat\_1~X0~X1=k2\_nat\_1~X1~X0)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v1\_int\_1}~{X0}})}}}\label{hyp:dgdgcdpfjgogehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_xboole\_0~X1))\end{array}
\label{hyp:dgdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdjdpfehfhchjgoghgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (l1\_turing\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_funct\_2~X1~k4\_numbers~\\
(u1\_turing\_1~X0)~(k9\_funct\_2~k4\_numbers~(u1\_turing\_1~X0))){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m2\_subset\_1~X3~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_subset\_1~\\
X4~k1\_numbers~k5\_numbers){\unicdbdjdcd}((r2\_turing\_1~(k3\_finseq\_4~k5\_numbers~\\
X2~X3~X4)~X0~X1){\unicdbdjdcd}((k1\_funct\_1~X1~X2=k6\_numbers){\unicdcdcdhd}((k1\_funct\_1~X1~\\
(k2\_nat\_1~(k2\_nat\_1~X2~X3)~np\_\_2)=k6\_numbers){\unicdcdcdhd}((k1\_funct\_1~X1~\\
(k2\_nat\_1~(k2\_nat\_1~(k2\_nat\_1~X2~X3)~X4)~np\_\_4)=k6\_numbers){\unicdcdcdhd}(\\
({\unicdcdadad} X5 .  (v1\_int\_1~X5){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X5~X2){\unicdcdcdhd}((\preoh r1\_xxreal\_0~\\
(k2\_nat\_1~(k2\_nat\_1~X2~X3)~np\_\_2)~X5){\unicdcdcdhd}(k1\_funct\_1~X1~X5{\unicdcdgdad}np\_\_1)))){\unicdcdcdhd}\\
({\unicdcdadad} X5 .  (v1\_int\_1~X5){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X5~(k2\_nat\_1~(k2\_nat\_1~\\
X2~X3)~np\_\_2)){\unicdcdcdhd}((\preoh r1\_xxreal\_0~(k2\_nat\_1~(k2\_nat\_1~(k2\_nat\_1~X2~\\
X3)~X4)~np\_\_4)~X5){\unicdcdcdhd}(k1\_funct\_1~X1~X5{\unicdcdgdad}np\_\_1)))))))))))))\end{array}$$
\end{theorem}
\end{document}
