\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{t35\_taxonom1 (TMV81gFyd5aRDDPvoXSniML5RUte2gDS63L)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_taxonom1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_taxonom1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_metric\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k3\_taxonom1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_taxonom1 : {{\iota}{\unicdbdjdcd}{{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k1\_partit1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k13\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_metric\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(v1\_xreal\_0~X1){\unicdbdjdcd}(r2\_relset\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~\\
(k3\_taxonom1~X0~X1)~(k1\_taxonom1~(u1\_struct\_0~X0)~(u1\_metric\_1~\\
X0)~X1)))\end{array}
\label{hyp:ehddddpfehbgihpgogpgngbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}((r2\_relset\_1~X0~X1~X2~X3){\unicdbdjded}(X2=X3))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdgcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_metric\_1~X0){\unicdbdjdcd}((v1\_funct\_1~(u1\_metric\_1~X0)){\unicdcdcdhd}\\
((v1\_funct\_2~(u1\_metric\_1~X0)~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(\\
u1\_struct\_0~X0))~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~(u1\_metric\_1~X0)~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0))~k1\_numbers)))))\end{array}
\label{hyp:egehpffhbdpfngfgehchjgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_metric\_1}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfngfgehchjgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v6\_metric\_1~X0){\unicdcdcdhd}((v8\_metric\_1~\\
X0){\unicdcdcdhd}(l1\_metric\_1~X0)))){\unicdbdjdcd}(m1\_subset\_1~(k4\_taxonom1~X0)~(k1\_zfmisc\_1~\\
(k1\_partit1~(u1\_struct\_0~X0))))\end{array}
\label{hyp:egehpflgedpfehbgihpgogpgngbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_metric\_1~X0)){\unicdcdcdhd}\\
(v1\_xreal\_0~X1)){\unicdbdjdcd}(m1\_subset\_1~(k3\_taxonom1~X0~X1)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))))\end{array}
\label{hyp:egehpflgddpfehbgihpgogpgngbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((v1\_funct\_1~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~\\
X0)~k1\_numbers)))){\unicdcdcdhd}(v1\_xreal\_0~X2))){\unicdbdjdcd}(m1\_subset\_1~(k1\_taxonom1~\\
X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))\end{array}
\label{hyp:egehpflgbdpfehbgihpgogpgngbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v6\_metric\_1~X0){\unicdcdcdhd}((v8\_metric\_1~\\
X0){\unicdcdcdhd}(l1\_metric\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_partit1~(u1\_struct\_0~X0)))){\unicdbdjdcd}((X1=k4\_taxonom1~X0){\unicdbdjded}({\unicdcdadad} X2 .  \\
(X2 \in X1){\unicdbdjded}({\unicdcdaddd} X3 .  ((\preoh v3\_xxreal\_0~X3){\unicdcdcdhd}(v1\_xreal\_0~X3)){\unicdcdcdhd}({\unicdcdaddd} X4 .  \\
((v1\_partfun1~X4~(u1\_struct\_0~X0)){\unicdcdcdhd}((v3\_relat\_2~X4){\unicdcdcdhd}((v8\_relat\_2~\\
X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~X0))))))){\unicdcdcdhd}((r2\_relset\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0)~X4~(k13\_lang1~(u1\_struct\_0~X0)~(k3\_taxonom1~X0~X3))){\unicdcdcdhd}(k8\_eqrel\_1~\\
(u1\_struct\_0~X0)~X4=X2)))))))\end{array}
\label{hyp:egidpfehbgihpgogpgngbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~k1\_numbers)))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_partit1~X0))){\unicdbdjdcd}(\\
(X2=k2\_taxonom1~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  (X3 \in X2){\unicdbdjded}({\unicdcdaddd} X4 .  ((\preoh v3\_xxreal\_0~\\
X4){\unicdcdcdhd}(v1\_xreal\_0~X4)){\unicdcdcdhd}({\unicdcdaddd} X5 .  ((v1\_partfun1~X5~X0){\unicdcdcdhd}((v3\_relat\_2~\\
X5){\unicdcdcdhd}((v8\_relat\_2~X5){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0)))))){\unicdcdcdhd}((r2\_relset\_1~X0~X0~X5~(k13\_lang1~X0~(k1\_taxonom1~X0~\\
X1~X4))){\unicdcdcdhd}(k8\_eqrel\_1~X0~X5=X3))))))))\end{array}
\label{hyp:egfdpfehbgihpgogpgngbd}
\end{equation}
\begin{theorem}\label{thm:ehddfdpfehbgihpgogpgngbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v6\_metric\_1~X0){\unicdcdcdhd}((v8\_metric\_1~\\
X0){\unicdcdcdhd}(l1\_metric\_1~X0)))){\unicdbdjdcd}(k4\_taxonom1~X0=k2\_taxonom1~(u1\_struct\_0~\\
X0)~(u1\_metric\_1~X0))\end{array}$$
\end{theorem}
\end{document}
