\documentclass{article}
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\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}
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\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t44\_borsuk\_7 (TMZUdxYavtVveqAAHXmKXU2r8qbXnYwTcvM)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k1\_euclid\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k12\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k21\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_euclid\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k18\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_complex1 : {\iota}$ be given.
Let $ k17\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_euclid\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
((k17\_euclid~X0=k8\_real\_1~(k12\_euclid~X0)~(k21\_sin\_cos~(k3\_euclid\_3~\\
X0))){\unicdcdcdhd}(k18\_euclid~X0=k8\_real\_1~(k12\_euclid~X0)~(k18\_sin\_cos~\\
(k3\_euclid\_3~X0))))\end{array}
\label{hyp:ehedddpfcgpgchdhfhlgpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(k1\_euclid\_3~(k2\_euclid\_3~X0)=X0)\end{array}
\label{hyp:ehcdpffgfhdgmgjgegpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(k2\_euclid\_3~X0=k2\_xcmplx\_0~(k17\_euclid~X0)~(k3\_xcmplx\_0~(k18\_euclid~\\
X0)~k7\_complex1))\end{array}
\label{hyp:egcdpffgfhdgmgjgegpfdd}
\end{equation}
\begin{theorem}\label{thm:ehededpfcgpgchdhfhlgpfhd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(X0=k1\_euclid\_3~(k2\_xcmplx\_0~(k8\_real\_1~(k12\_euclid~X0)~(k21\_sin\_cos~\\
(k3\_euclid\_3~X0)))~(k3\_xcmplx\_0~(k8\_real\_1~(k12\_euclid~X0)~(k18\_sin\_cos~\\
(k3\_euclid\_3~X0)))~k7\_complex1)))\end{array}$$
\end{theorem}
\end{document}
