\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{t20\_nat\_3 (TMMEeTYk3tFC6zx89F345T4QPFkdE7AeN9g)}
\maketitle
Let $ k8\_nat\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k16\_pre\_poly : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k21\_rvsum\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k1\_polynom2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\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 $ k7\_nat\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k19\_rvsum\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_numbers : {\iota}$ be given.
Let $ k20\_rvsum\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k13\_pre\_poly : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_pre\_poly : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k14\_pre\_poly : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_uproots : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k8\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v4\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{{k21\_rvsum\_1}~{({{k6\_finseq\_1}~{k1\_numbers}})}}={np\_\_1}}\label{hyp:ehjdedpfchghdhfhngpfbd}
\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}
{{\unicdcdadad} X0 .  {{{{k1\_polynom2}~{X0}}~{({{k16\_pre\_poly}~{X0}})}}={k1\_xboole\_0}}}\label{hyp:ehbdidpfcgbghgpgchegfgch}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\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}(k8\_nat\_3~X0~X1=k7\_nat\_3~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfogbgehpfdd}
\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 .  (m1\_finseq\_1~X0~k1\_numbers){\unicdbdjdcd}(k21\_rvsum\_1~X0=k19\_rvsum\_1~\\
X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdbdpfchghdhfhngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_finseq\_1~X0~k2\_numbers){\unicdbdjdcd}(k20\_rvsum\_1~X0=k19\_rvsum\_1~\\
X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdadpfchghdhfhngpfbd}
\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}
{{\unicdcdadad} X0 .  {{{k15\_pre\_poly}~{X0}}={{k14\_pre\_poly}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdfdpfahchfgpfahpgmgjh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {\preoh{{{v1\_xboole\_0}~{({{k14\_pre\_poly}~{X0}})}}}}}\label{hyp:ggdgcdedpfahchfgpfahpgmgjh}
\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 .  ((v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_relat\_1~X1)){\unicdbdjdcd}((\\
v1\_xboole\_0~(k3\_relat\_1~X0~X1)){\unicdcdcdhd}(v1\_relat\_1~(k3\_relat\_1~X0~X1)))\end{array}
\label{hyp:ggdgbdcdpfchfgmgbgehpfbd}
\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){\unicdbdjdcd}(m1\_subset\_1~X2~X0))\end{array}
\label{hyp:egehpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m2\_finseq\_1~X1~X0){\unicdbdjdcd}((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_finseq\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
X0)))))\end{array}
\label{hyp:egehpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{m2\_finseq\_1}~{({{k6\_finseq\_1}~{X0}})}}~{X0}}}\label{hyp:egehpflggdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_finseq\_1~X0~k2\_numbers){\unicdbdjdcd}(m1\_subset\_1~(k20\_rvsum\_1~\\
X0)~k2\_numbers)\end{array}
\label{hyp:egehpflgcdadpfchghdhfhngpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_finset\_1}~{X0}})}{\unicdbdjdcd}{({{{m2\_finseq\_1}~{({{k1\_uproots}~{X0}})}}~{X0}})}}}\label{hyp:egehpflgbdpffhahchpgpgehdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  m2\_subset\_1~(k16\_pre\_poly~X0)~(k14\_pre\_poly~X0)~(k15\_pre\_poly~\\
X0)\end{array}
\label{hyp:egehpflgbdgdpfahchfgpfahpgmgjh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  m1\_subset\_1~(k15\_pre\_poly~X0)~(k1\_zfmisc\_1~(k14\_pre\_poly~\\
X0))\end{array}
\label{hyp:egehpflgbdfdpfahchfgpfahpgmgjh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k6\_finseq\_1}~{X0}}={k1\_xboole\_0}}}\label{hyp:eggdpfggjgogdhfgbhpfbd}
\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}((v1\_valued\_0~X1){\unicdcdcdhd}(v2\_pre\_poly~\\
X1)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_xcmplx\_0~X2){\unicdbdjdcd}((X2=k7\_nat\_3~X0~X1){\unicdbdjded}\\
({\unicdcdaddd} X3 .  (m2\_finseq\_1~X3~k2\_numbers){\unicdcdcdhd}((X2=k20\_rvsum\_1~X3){\unicdcdcdhd}\\
(X3=k3\_relat\_1~(k1\_uproots~(k13\_pre\_poly~X1))~X1)))))\end{array}
\label{hyp:egfdpfogbgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k16\_pre\_poly}~{X0}}={{{{k8\_funcop\_1}~{k5\_numbers}}~{X0}}~{k6\_numbers}}}}\label{hyp:egbdddpfahchfgpfahpgmgjh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k15\_pre\_poly~\\
X0))){\unicdbdjdcd}(v4\_funct\_1~X1)\end{array}
\label{hyp:dgdgjdpfahchfgpfahpgmgjh}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  (v4\_funct\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}(\\
(v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)))\end{array}
\label{hyp:dgdgidpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v3\_valued\_0~X0)){\unicdbdjdcd}((v1\_relat\_1~\\
X0){\unicdcdcdhd}(v1\_valued\_0~X0))\end{array}
\label{hyp:dgdggdpfghbgmgfhfgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X0))){\unicdbdjdcd}(v1\_xboole\_0~X2))\end{array}
\label{hyp:dgdgedpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k2\_numbers}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgddpfihdgngahmgihpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_finset\_1}~{X0}})}}}\label{hyp:dgdgbdpfggjgogdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k15\_pre\_poly~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X1){\unicdbdjdcd}((v1\_partfun1~\\
X2~X0){\unicdcdcdhd}((v4\_valued\_0~X2){\unicdcdcdhd}(v2\_pre\_poly~X2))))\end{array}
\label{hyp:dgdgbdbdpfahchfgpfahpgmgjh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k15\_pre\_poly~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X1){\unicdbdjdcd}(v4\_relat\_1~X2~X0))\end{array}
\label{hyp:dgdgbdadpfahchfgpfahpgmgjh}
\end{equation}
\begin{theorem}\label{thm:ehcdadpfogbgehpfdd}
${{\unicdcdadad} X0 .  {{{{k8\_nat\_3}~{X0}}~{({{k16\_pre\_poly}~{X0}})}}={np\_\_1}}}$.
\end{theorem}
\end{document}
