\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\preoh[1]{\lnot #1}
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\begin{document}
\title{t17\_moebius1 (TMNJqgoU35kWyKikbD3sFFsijEvdLZXV3NQ)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_int\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k11\_nat\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_polynom2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_newton : {\iota}$ be given.
Let $ k13\_nat\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_newton : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k13\_pre\_poly : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_nat\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_poly : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k10\_nat\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}((r1\_xxreal\_0~\\
X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X0){\unicdcdcdid}((v2\_xxreal\_0~X1){\unicdcdcdid}(v3\_xxreal\_0~X0)))))\end{array}
\label{hyp:ehgdpfchfgbgmg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh \\
v1\_xboole\_0~X1){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}((k11\_nat\_3~X1~X0{\unicdcdgdad}k6\_numbers){\unicdbdjdcd}\\
(k1\_seq\_1~(k13\_nat\_3~X1)~X0=k1\_newton~X0~(k11\_nat\_3~X1~X0))))\end{array}
\label{hyp:ehfdgdpfogbgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh \\
v1\_xboole\_0~X1){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}((k11\_nat\_3~X1~X0=k6\_numbers){\unicdbdjdcd}\\
(k1\_seq\_1~(k13\_nat\_3~X1)~X0=k6\_numbers)))\end{array}
\label{hyp:ehfdfdpfogbgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (X1 \in k13\_pre\_poly~(k12\_nat\_3~\\
X0)){\unicdbdjdcd}((v7\_ordinal1~X1){\unicdcdcdhd}(v1\_int\_2~X1)))\end{array}
\label{hyp:ehddedpfogbgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v3\_valued\_0~\\
X0))){\unicdbdjdcd}(k1\_seq\_1~X0~X1=k1\_funct\_1~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}((v4\_valued\_0~X1){\unicdcdcdhd}(v2\_pre\_poly~\\
X1)))))){\unicdbdjdcd}(k1\_polynom2~X0~X1=k13\_pre\_poly~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfahpgmgjhogpgngcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}(\\
k11\_nat\_3~X0~X1=k10\_nat\_3~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdbdpfogbgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v7\_ordinal1~X0)){\unicdbdjdcd}((v1\_relat\_1~\\
(k13\_nat\_3~X0)){\unicdcdcdhd}((v4\_relat\_1~(k13\_nat\_3~X0)~k10\_newton){\unicdcdcdhd}((v1\_funct\_1~\\
(k13\_nat\_3~X0)){\unicdcdcdhd}((v1\_partfun1~(k13\_nat\_3~X0)~k10\_newton){\unicdcdcdhd}((\\
v4\_valued\_0~(k13\_nat\_3~X0)){\unicdcdcdhd}(v2\_pre\_poly~(k13\_nat\_3~X0)))))))\end{array}
\label{hyp:ggdgcdbdpfogbgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v7\_ordinal1~X0)){\unicdcdcdhd}\\
(v7\_ordinal1~X1)){\unicdbdjdcd}(\preoh v1\_xboole\_0~(k1\_newton~X0~X1))\end{array}
\label{hyp:ggdgbdpfogbgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v7\_ordinal1~X0)){\unicdbdjdcd}((v1\_relat\_1~\\
(k12\_nat\_3~X0)){\unicdcdcdhd}((v4\_relat\_1~(k12\_nat\_3~X0)~k10\_newton){\unicdcdcdhd}((v1\_funct\_1~\\
(k12\_nat\_3~X0)){\unicdcdcdhd}((v1\_partfun1~(k12\_nat\_3~X0)~k10\_newton){\unicdcdcdhd}(v2\_pre\_poly~\\
(k12\_nat\_3~X0))))))\end{array}
\label{hyp:ggdgbdhdpfogbgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((v1\_relat\_1~(k12\_nat\_3~X0)){\unicdcdcdhd}((\\
v4\_relat\_1~(k12\_nat\_3~X0)~k10\_newton){\unicdcdcdhd}((v1\_funct\_1~(k12\_nat\_3~\\
X0)){\unicdcdcdhd}((v1\_partfun1~(k12\_nat\_3~X0)~k10\_newton){\unicdcdcdhd}(v4\_valued\_0~\\
(k12\_nat\_3~X0))))))\end{array}
\label{hyp:ggdgbdgdpfogbgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}(\\
v7\_ordinal1~(k10\_nat\_3~X0~X1))\end{array}
\label{hyp:egehpflgbdadpfogbgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v7\_ordinal1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~k10\_newton){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}\\
(v1\_partfun1~X1~k10\_newton)))){\unicdbdjdcd}((X1=k13\_nat\_3~X0){\unicdbdjded}((k13\_pre\_poly~\\
X1=k1\_polynom2~k10\_newton~(k12\_nat\_3~X0)){\unicdcdcdhd}({\unicdcdadad} X2 .  (v7\_ordinal1~\\
X2){\unicdbdjdcd}((X2 \in k1\_polynom2~k10\_newton~(k12\_nat\_3~X0)){\unicdbdjdcd}(k1\_funct\_1~\\
X1~X2=k1\_newton~X2~(k11\_nat\_3~X0~X2)))))))\end{array}
\label{hyp:egjdpfogbgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (X1=\\
k13\_pre\_poly~X0){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}(k1\_funct\_1~X0~X2{\unicdcdgdad}k6\_numbers)))\end{array}
\label{hyp:eghdpfahchfgpfahpgmgjh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_tarski~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X0){\unicdbdjdcd}\\
(X2 \in X1))\end{array}
\label{hyp:egddpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v4\_valued\_0~X0)){\unicdbdjdcd}((v1\_relat\_1~\\
X0){\unicdcdcdhd}(v3\_valued\_0~X0))\end{array}
\label{hyp:dgdgidpfghbgmgfhfgegpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdghdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v2\_xxreal\_0~X0)){\unicdbdjdcd}((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((v1\_xxreal\_0~X0){\unicdcdcdhd}(\preoh v3\_xxreal\_0~X0)))\end{array}
\label{hyp:dgdgddpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{({{v7\_ordinal1}~{X0}})}{\unicdcdcdhd}{({\preoh{{{v3\_xxreal\_0}~{X0}}}})}})}}}\label{hyp:dgdgddpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgcdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgcdpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)))\end{array}
\label{hyp:dgdgbdpfogbgehpfdd}
\end{equation}
\begin{theorem}\label{thm:ehbdhdpfngpgfgcgjgfhdhbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v7\_ordinal1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}(({\unicdcdadad} X2 .  ((v7\_ordinal1~\\
X2){\unicdcdcdhd}(v1\_int\_2~X2)){\unicdbdjdcd}(r1\_xxreal\_0~(k11\_nat\_3~X0~X2)~(k11\_nat\_3~\\
X1~X2))){\unicdbdjdcd}(r1\_tarski~(k1\_polynom2~k10\_newton~(k13\_nat\_3~X0))~(\\
k1\_polynom2~k10\_newton~(k13\_nat\_3~X1)))))\end{array}$$
\end{theorem}
\end{document}
