\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{t67\_complex2 (TMTeC8GTZXzzcPs6DfN8rpCmiyBZGxLZxzT)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_numbers : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k3\_complex2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k2\_complex2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k32\_sin\_cos : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}(\preoh (X0{\unicdcdgdad}\\
k6\_numbers){\unicdcdcdhd}((X1{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}(k3\_complex2~X0~X1{\unicdcdgdad}k3\_complex2~\\
(k2\_complex2~X0~X2)~(k2\_complex2~X1~X2))))))\end{array}
\label{hyp:ehgdfdpfdgpgngahmgfgihcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_numbers){\unicdbdjdcd}(k2\_complex2~X0~k32\_sin\_cos=\\
k10\_complex1~X0)\end{array}
\label{hyp:ehgdadpfdgpgngahmgfgihcd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k32\_sin\_cos}}~{k1\_numbers}}\label{hyp:egehpflgddcdpfdhjgogpfdgpgdh}
\end{equation}
\begin{theorem}\label{thm:ehgdhdpfdgpgngahmgfgihcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k2\_numbers){\unicdbdjdcd}(\preoh (X0{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}((X1{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}(k3\_complex2~\\
X0~X1{\unicdcdgdad}k3\_complex2~(k10\_complex1~X0)~(k10\_complex1~X1)))))\end{array}$$
\end{theorem}
\end{document}
