\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{t31\_polynom1 (TMKasyvXzXCD3hvytcJSwWiq9BU8AXWmFqv)}
\maketitle
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_polynom1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_polynom1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v36\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ k15\_pre\_poly : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_polynom1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ k1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_polynom1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_polynom1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_polynom1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v3\_ordinal1~X0){\unicdcdcdhd}((\preoh v7\_struct\_0~X1){\unicdcdcdhd}\\
((v13\_algstr\_0~X1){\unicdcdcdhd}((v3\_vectsp\_1~X1){\unicdcdcdhd}((v5\_vectsp\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~\\
X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}(l6\_algstr\_0~X1)))))))){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k11\_polynom1~X0~X1)){\unicdcdcdhd}((v36\_algstr\_0~(k11\_polynom1~X0~X1)){\unicdcdcdhd}(\\
l6\_algstr\_0~(k11\_polynom1~X0~X1))))\end{array}
\label{hyp:egehpflgbdbdpfahpgmgjhogpgngbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v7\_struct\_0~X1){\unicdcdcdhd}\\
((v13\_algstr\_0~X1){\unicdcdcdhd}((v3\_vectsp\_1~X1){\unicdcdcdhd}((v5\_vectsp\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~\\
X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}(l6\_algstr\_0~X1))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (\\
(\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v36\_algstr\_0~X2){\unicdcdcdhd}(l6\_algstr\_0~X2))){\unicdbdjdcd}((\\
X2=k11\_polynom1~X0~X1){\unicdbdjded}(({\unicdcdadad} X3 .  (X3 \in u1\_struct\_0~X2){\unicdbdjded}((v1\_funct\_1~\\
X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k15\_pre\_poly~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}((v1\_polynom1~\\
X3~(k15\_pre\_poly~X0)~X1){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k15\_pre\_poly~X0)~(u1\_struct\_0~X1)))))))){\unicdcdcdhd}(({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
X2)){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~(k15\_pre\_poly~\\
X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}((v1\_polynom1~X5~(k15\_pre\_poly~X0)~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k15\_pre\_poly~X0)~(\\
u1\_struct\_0~X1))))))){\unicdbdjdcd}({\unicdcdadad} X6 .  ((v1\_funct\_1~X6){\unicdcdcdhd}((v1\_funct\_2~\\
X6~(k15\_pre\_poly~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}((v1\_polynom1~X6~(k15\_pre\_poly~\\
X0)~X1){\unicdcdcdhd}(m1\_subset\_1~X6~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k15\_pre\_poly~\\
X0)~(u1\_struct\_0~X1))))))){\unicdbdjdcd}(((X3=X5){\unicdcdcdhd}(X4=X6)){\unicdbdjdcd}(k1\_algstr\_0~\\
X2~X3~X4=k4\_polynom1~X0~X1~X5~X6)))))){\unicdcdcdhd}(({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
X2)){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~(k15\_pre\_poly~\\
X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}((v1\_polynom1~X5~(k15\_pre\_poly~X0)~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k15\_pre\_poly~X0)~(\\
u1\_struct\_0~X1))))))){\unicdbdjdcd}({\unicdcdadad} X6 .  ((v1\_funct\_1~X6){\unicdcdcdhd}((v1\_funct\_2~\\
X6~(k15\_pre\_poly~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}((v1\_polynom1~X6~(k15\_pre\_poly~\\
X0)~X1){\unicdcdcdhd}(m1\_subset\_1~X6~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k15\_pre\_poly~\\
X0)~(u1\_struct\_0~X1))))))){\unicdbdjdcd}(((X3=X5){\unicdcdcdhd}(X4=X6)){\unicdbdjdcd}(k6\_algstr\_0~\\
X2~X3~X4=k9\_polynom1~X0~X1~X5~X6)))))){\unicdcdcdhd}((k4\_struct\_0~X2=k7\_polynom1~\\
X0~X1){\unicdcdcdhd}(k5\_struct\_0~X2=k8\_polynom1~X0~X1))))))))\end{array}
\label{hyp:egbdadpfahpgmgjhogpgngbd}
\end{equation}
\begin{theorem}\label{thm:ehddbdpfahpgmgjhogpgngbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((\preoh v7\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v3\_group\_1~X1){\unicdcdcdhd}((v3\_vectsp\_1~\\
X1){\unicdcdcdhd}((v5\_vectsp\_1~X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}\\
((v4\_rlvect\_1~X1){\unicdcdcdhd}(l6\_algstr\_0~X1)))))))))){\unicdbdjdcd}(k5\_struct\_0~(\\
k11\_polynom1~X0~X1)=k8\_polynom1~X0~X1))\end{array}$$
\end{theorem}
\end{document}
