\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{t22\_ratfunc1 (TMHB64BTuZAEV486YyxYpWgtK2h5vGHpbTY)}
\maketitle
Let $ v7\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v33\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_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 $ v1\_vectsp\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_ratfunc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_ratfunc1 : {{\iota}{\unicdbdjdcd}{{\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 $ k5\_numbers : {\iota}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_algseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_ratfunc1 : {{\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 $ k3\_ratfunc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k13\_polynom3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_ratfunc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_ratfunc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v5\_ratfunc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k14\_polynom3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_group\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_ratfunc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_hurwitz : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k11\_ratfunc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_ratfunc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_ratfunc1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}\\
((v33\_algstr\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}((v4\_vectsp\_1~\\
X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}\\
((v4\_rlvect\_1~X0){\unicdcdcdhd}((v1\_vectsp\_2~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdcdcdhd}\\
(m1\_ratfunc1~X1~X0)){\unicdbdjdcd}(m1\_ratfunc1~(k6\_ratfunc1~X0~X1)~X0)\end{array}
\label{hyp:egehpflggdpfchbgehggfhogdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v33\_algstr\_0~\\
X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}((\\
v5\_vectsp\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~\\
X0){\unicdcdcdhd}((v1\_vectsp\_2~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_ratfunc1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_ratfunc1~X2~X0){\unicdbdjdcd}(((\preoh v4\_ratfunc1~\\
X1~X0){\unicdbdjdcd}((X2=k11\_ratfunc1~X0~X1){\unicdbdjded}({\unicdcdaddd} X3 .  (m1\_ratfunc1~X3~X0){\unicdcdcdhd}\\
({\unicdcdaddd} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~k5\_numbers~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((v1\_algseq\_1~X4~X0){\unicdcdcdhd}((\preoh v1\_ratfunc1~X4~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(u1\_struct\_0~X0)))))))){\unicdcdcdhd}\\
((X1=k3\_ratfunc1~X0~(k13\_polynom3~X0~X4~(k4\_ratfunc1~X0~X3))~(k13\_polynom3~\\
X0~X4~(k5\_ratfunc1~X0~X3))){\unicdcdcdhd}((v5\_ratfunc1~X3~X0){\unicdcdcdhd}((X2=k6\_ratfunc1~\\
X0~X3){\unicdcdcdhd}({\unicdcdaddd} X5 .  (m2\_finseq\_1~X5~(u1\_struct\_0~(k14\_polynom3~\\
X0))){\unicdcdcdhd}((X4=k3\_group\_4~(k14\_polynom3~X0)~X5){\unicdcdcdhd}({\unicdcdadad} X6 .  (m1\_subset\_1~\\
X6~k5\_numbers){\unicdbdjdcd}(\preoh (X6 \in k4\_finseq\_1~X5){\unicdcdcdhd}({\unicdcdadad} X7 .  (m1\_subset\_1~\\
X7~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (r1\_ratfunc1~X0~(k4\_ratfunc1~X0~X1)~(k5\_ratfunc1~\\
X0~X1)~X7){\unicdcdcdhd}(k1\_funct\_1~X5~X6=k3\_hurwitz~X0~X7~np\_\_1)))))))))))))){\unicdcdcdhd}\\
((v4\_ratfunc1~X1~X0){\unicdbdjdcd}((X2=k11\_ratfunc1~X0~X1){\unicdbdjded}(X2=k7\_ratfunc1~\\
X0))))))\end{array}
\label{hyp:egbdhdpfchbgehggfhogdgbd}
\end{equation}
\begin{theorem}\label{thm:ehcdcdpfchbgehggfhogdgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v33\_algstr\_0~\\
X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}((\\
v5\_vectsp\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~\\
X0){\unicdcdcdhd}((v1\_vectsp\_2~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v4\_ratfunc1~X1~X0){\unicdcdcdhd}(m1\_ratfunc1~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_ratfunc1~\\
X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~k5\_numbers~\\
(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_algseq\_1~X3~X0){\unicdcdcdhd}((\preoh v1\_ratfunc1~X3~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(u1\_struct\_0~\\
X0)))))))){\unicdbdjdcd}(((X1=k3\_ratfunc1~X0~(k13\_polynom3~X0~X3~(k4\_ratfunc1~\\
X0~X2))~(k13\_polynom3~X0~X3~(k5\_ratfunc1~X0~X2))){\unicdcdcdhd}(v5\_ratfunc1~\\
X2~X0)){\unicdbdjdcd}(({\unicdcdadad} X4 .  (m2\_finseq\_1~X4~(u1\_struct\_0~(k14\_polynom3~\\
X0))){\unicdbdjdcd}(\preoh (X3=k3\_group\_4~(k14\_polynom3~X0)~X4){\unicdcdcdhd}({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~k5\_numbers){\unicdbdjdcd}(\preoh (X5 \in k4\_finseq\_1~X4){\unicdcdcdhd}({\unicdcdadad} X6 .  (m1\_subset\_1~\\
X6~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (r1\_ratfunc1~X0~(k4\_ratfunc1~X0~X1)~(k5\_ratfunc1~\\
X0~X1)~X6){\unicdcdcdhd}(k1\_funct\_1~X4~X5=k3\_hurwitz~X0~X6~np\_\_1))))))){\unicdcdcdid}(k11\_ratfunc1~\\
X0~X1=k6\_ratfunc1~X0~X2))))))\end{array}$$
\end{theorem}
\end{document}
