\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{t44\_uniroots (TMFNqhfCNSBfHBUqwkk26mJUMhCWwDfY7uY)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_complfld : {\iota}$ be given.
Let $ k2\_polynom4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_uniroots : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_newton : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k2\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k4\_group\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v36\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_numbers : {\iota}$ be given.
Let $ u1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k27\_binop\_2 : {\iota}$ be given.
Let $ u2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k29\_binop\_2 : {\iota}$ be given.
Let $ k5\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_complex1 : {\iota}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_complex1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~k1\_complfld)){\unicdbdjdcd}(\preoh (m1\_subset\_1~X1~\\
k1\_numbers){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}(\preoh (X2=\\
X1){\unicdcdcdhd}(k2\_binop\_1~(u1\_struct\_0~k1\_complfld)~k5\_numbers~(u1\_struct\_0~\\
k1\_complfld)~(k4\_group\_1~k1\_complfld)~X1~X0=k2\_newton~X2~X0)))))\end{array}
\label{hyp:ehedddpffhogjgchpgpgehdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m2\_subset\_1~X0~k1\_numbers~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~k1\_complfld)){\unicdbdjdcd}(k2\_polynom4~\\
k1\_complfld~(k4\_uniroots~X0~k1\_complfld)~X1=k4\_binop\_2~(k2\_binop\_1~\\
(u1\_struct\_0~k1\_complfld)~k5\_numbers~(u1\_struct\_0~k1\_complfld)~\\
(k4\_group\_1~k1\_complfld)~X1~X0)~np\_\_1))\end{array}
\label{hyp:ehedbdpffhogjgchpgpgehdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xcmplx\_0~X0){\unicdcdcdhd}(v1\_xcmplx\_0~X1)){\unicdbdjdcd}(\\
k4\_binop\_2~X0~X1=k6\_xcmplx\_0~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfcgjgogpgahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}(v1\_xreal\_0~X1)){\unicdbdjdcd}(k10\_binop\_2~\\
X0~X1=k6\_xcmplx\_0~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdadpfcgjgogpgahpfcd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_finset\_1}~{k4\_ordinal1}}}}\label{hyp:ggdghdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v6\_membered}~{k4\_ordinal1}}\label{hyp:ggdggdpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_numbers}}}}\label{hyp:ggdgbdpfogfhngcgfgchdh}
\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~k1\_numbers){\unicdcdcdhd}(v7\_ordinal1~\\
X1)){\unicdbdjdcd}(m1\_subset\_1~(k2\_newton~X0~X1)~k1\_numbers)\end{array}
\label{hyp:egehpflgcdpfogfghhehpgog}
\end{equation}
Assume the following.
\begin{equation}
{{({{v36\_algstr\_0}~{k1\_complfld}})}{\unicdcdcdhd}{({{l6\_algstr\_0}~{k1\_complfld}})}}\label{hyp:egehpflgbdpfdgpgngahmgggmgeg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjded}{({{X0} \in {k2\_numbers}})}}}\label{hyp:egcdpfihdgngahmgihpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v36\_algstr\_0~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)){\unicdbdjdcd}((X0=k1\_complfld){\unicdbdjded}\\
((u1\_struct\_0~X0=k2\_numbers){\unicdcdcdhd}((u1\_algstr\_0~X0=k27\_binop\_2){\unicdcdcdhd}\\
((u2\_algstr\_0~X0=k29\_binop\_2){\unicdcdcdhd}((k5\_struct\_0~X0=k6\_complex1){\unicdcdcdhd}\\
(k4\_struct\_0~X0=k5\_complex1))))))\end{array}
\label{hyp:egbdpfdgpgngahmgggmgeg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgddpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgbdpfihdgngahmgihpfad}
\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 .  (v6\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v7\_ordinal1~X1))\end{array}
\label{hyp:dgdgbdhdpfngfgngcgfgchfgeg}
\end{equation}
\begin{theorem}\label{thm:ehededpffhogjgchpgpgehdh}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m2\_subset\_1~X0~k1\_numbers~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k1\_numbers){\unicdbdjdcd}({\unicdcdaddd} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~k1\_complfld)){\unicdcdcdhd}((X2=X1){\unicdcdcdhd}(k2\_polynom4~k1\_complfld~\\
(k4\_uniroots~X0~k1\_complfld)~X2=k10\_binop\_2~(k2\_newton~X1~X0)~\\
np\_\_1))))\end{array}$$
\end{theorem}
\end{document}
