\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{t17\_taylor\_1 (TMFVsqWQ6Z5Z2Hpx1QJpu4YfU9cm3eLANng)}
\maketitle
Let $ r2\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_partfun2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k24\_sin\_cos : {\iota}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_subset\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_funct\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_limfunc1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v2\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers))))){\unicdbdjdcd}(((r1\_tarski~\\
(k2\_subset\_1~k1\_numbers)~(k1\_relset\_1~k1\_numbers~X0)){\unicdcdcdhd}(r2\_fdiff\_1~\\
X0~(k2\_subset\_1~k1\_numbers))){\unicdbdjdcd}((({\unicdcdaddd} X1 .  (m1\_subset\_1~X1~\\
k1\_numbers){\unicdcdcdhd}(r1\_xxreal\_0~(k1\_fdiff\_1~X0~X1)~k6\_numbers)){\unicdcdcdhd}({\unicdcdaddd} X1 .  \\
(m1\_subset\_1~X1~k1\_numbers){\unicdcdcdhd}(r1\_xxreal\_0~k6\_numbers~(k1\_fdiff\_1~\\
X0~X1)))){\unicdcdcdid}((v2\_funct\_1~X0){\unicdcdcdhd}((r2\_fdiff\_1~(k2\_partfun2~k1\_numbers~\\
k1\_numbers~X0)~(k1\_relset\_1~k1\_numbers~(k2\_partfun2~k1\_numbers~\\
k1\_numbers~X0))){\unicdcdcdhd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k1\_numbers){\unicdbdjdcd}((\\
X1 \in k1\_relset\_1~k1\_numbers~(k2\_partfun2~k1\_numbers~k1\_numbers~\\
X0)){\unicdbdjdcd}(k1\_fdiff\_1~(k2\_partfun2~k1\_numbers~k1\_numbers~X0)~X1=k10\_real\_1~\\
np\_\_1~(k1\_fdiff\_1~X0~(k1\_seq\_1~(k2\_partfun2~k1\_numbers~k1\_numbers~\\
X0)~X1)))))))))\end{array}
\label{hyp:ehedfdpfggegjgggggpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}(((\\
v2\_funct\_1~X1){\unicdcdcdhd}(X0 \in k10\_xtuple\_0~X1)){\unicdbdjdcd}((X0=k1\_funct\_1~X1~(k1\_funct\_1~\\
(k2\_funct\_1~X1)~X0)){\unicdcdcdhd}(X0=k1\_funct\_1~(k3\_relat\_1~(k2\_funct\_1~\\
X1)~X1)~X0)))\end{array}
\label{hyp:ehddfdpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}((v2\_funct\_1~X0){\unicdbdjdcd}\\
((k10\_xtuple\_0~X0=k9\_xtuple\_0~(k2\_funct\_1~X0)){\unicdcdcdhd}(k9\_xtuple\_0~\\
X0=k10\_xtuple\_0~(k2\_funct\_1~X0))))\end{array}
\label{hyp:ehddddpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v2\_funct\_1~k24\_sin\_cos){\unicdcdcdhd}((r2\_fdiff\_1~k24\_sin\_cos~k1\_numbers){\unicdcdcdhd}\\
((r2\_fdiff\_1~k24\_sin\_cos~(k2\_subset\_1~k1\_numbers)){\unicdcdcdhd}(({\unicdcdadad} X0 .  \\
(m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(k1\_fdiff\_1~k24\_sin\_cos~X0=k1\_seq\_1~\\
k24\_sin\_cos~X0)){\unicdcdcdhd}(({\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(\\
\preoh r1\_xxreal\_0~(k1\_fdiff\_1~k24\_sin\_cos~X0)~k6\_numbers)){\unicdcdcdhd}((k1\_relset\_1~\\
k1\_numbers~k24\_sin\_cos=k2\_subset\_1~k1\_numbers){\unicdcdcdhd}((k1\_relset\_1~\\
k1\_numbers~k24\_sin\_cos=k2\_subset\_1~k1\_numbers){\unicdcdcdhd}(k2\_relset\_1~\\
k1\_numbers~k24\_sin\_cos=k3\_limfunc1~k6\_numbers)))))))\end{array}
\label{hyp:ehbdgdpfehbgjhmgpgchpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r1\_tarski}~{X0}}~{X0}}}}\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v2\_funct\_1~\\
X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))))){\unicdbdjdcd}(k2\_partfun2~\\
X0~X1~X2=k2\_funct\_1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfahbgchehggfhogcd}
\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)){\unicdbdjdcd}(\\
k1\_relset\_1~X0~X1=k9\_xtuple\_0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k24\_sin\_cos){\unicdcdcdhd}((v2\_funct\_1~k24\_sin\_cos){\unicdcdcdhd}(v1\_funct\_2~\\
k24\_sin\_cos~k1\_numbers~k1\_numbers))\end{array}
\label{hyp:ggdgbdpfehbgjhmgpgchpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v2\_funct\_1~\\
X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))))){\unicdbdjdcd}((v1\_funct\_1~\\
(k2\_partfun2~X0~X1~X2)){\unicdcdcdhd}(m1\_subset\_1~(k2\_partfun2~X0~X1~X2)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X1~X0))))\end{array}
\label{hyp:egehpflgcdpfahbgchehggfhogcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}((v1\_relat\_1~(\\
k2\_funct\_1~X0)){\unicdcdcdhd}(v1\_funct\_1~(k2\_funct\_1~X0)))\end{array}
\label{hyp:egehpflgcdpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k24\_sin\_cos){\unicdcdcdhd}((v1\_funct\_2~k24\_sin\_cos~k1\_numbers~\\
k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~k24\_sin\_cos~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers))))\end{array}
\label{hyp:egehpflgcdedpfdhjgogpfdgpgdh}
\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}(m1\_subset\_1~(k1\_seq\_1~X0~X1)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdpfdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k2\_subset\_1}~{X0}}={X0}}}\label{hyp:egddpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v5\_relat\_1~X0~k1\_numbers)){\unicdbdjdcd}((v1\_relat\_1~\\
X0){\unicdcdcdhd}(v3\_valued\_0~X0))\end{array}
\label{hyp:dgdgddadpfghbgmgfhfgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}(v5\_relat\_1~X2~X1))\end{array}
\label{hyp:dgdgcdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v1\_relat\_1~X2)\end{array}
\label{hyp:dgdgbdpfchfgmgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdhdpfehbgjhmgpgchpfbd}
$$\begin{array}{c}(r2\_fdiff\_1~(k2\_partfun2~k1\_numbers~k1\_numbers~k24\_sin\_cos)~\\
(k1\_relset\_1~k1\_numbers~(k2\_partfun2~k1\_numbers~k1\_numbers~k24\_sin\_cos))){\unicdcdcdhd}\\
({\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((X0 \in k1\_relset\_1~k1\_numbers~(k2\_partfun2~\\
k1\_numbers~k1\_numbers~k24\_sin\_cos)){\unicdbdjdcd}(k1\_fdiff\_1~(k2\_partfun2~\\
k1\_numbers~k1\_numbers~k24\_sin\_cos)~X0=k10\_real\_1~np\_\_1~X0)))\end{array}$$
\end{theorem}
\end{document}
