\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\begin{document}
\title{t80\_complsp2 (TMHZF6zVtocikmN1rnGRaJvr2cwhdFTbXzK)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_numbers : {\iota}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_complsp2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_seq\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k12\_seq\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_1~\\
X1~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~k2\_numbers){\unicdbdjdcd}((k3\_finseq\_1~\\
X1=k3\_finseq\_1~X2){\unicdbdjdcd}(k8\_complsp2~(k12\_seq\_4~X1~X0)~X2=k5\_binop\_2~\\
X0~(k8\_complsp2~X1~X2)))))\end{array}
\label{hyp:ehhdidpfdgpgngahmgdhahcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_1~X0~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_1~\\
X1~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~k2\_numbers){\unicdbdjdcd}(((k3\_finseq\_1~\\
X0=k3\_finseq\_1~X1){\unicdcdcdhd}(k3\_finseq\_1~X1=k3\_finseq\_1~X2)){\unicdbdjdcd}(k8\_complsp2~\\
(k9\_seq\_4~X0~X1)~X2=k3\_binop\_2~(k8\_complsp2~X0~X2)~(k8\_complsp2~\\
X1~X2)))))\end{array}
\label{hyp:ehgdgdpfdgpgngahmgdhahcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xcmplx\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_1~X1~k2\_numbers){\unicdbdjdcd}\\
(k3\_finseq\_1~(k12\_seq\_4~X1~X0)=k3\_finseq\_1~X1))\end{array}
\label{hyp:ehddpfdgpgngahmgdhahcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_finseq\_1~X0~k2\_numbers){\unicdcdcdhd}(v1\_xcmplx\_0~\\
X1)){\unicdbdjdcd}(m2\_finseq\_1~(k12\_seq\_4~X0~X1)~k2\_numbers)\end{array}
\label{hyp:egehpflgbdcdpfdhfgbhpfed}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k2\_numbers}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgddpfihdgngahmgihpfad}
\end{equation}
\begin{theorem}\label{thm:ehidadpfdgpgngahmgdhahcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m2\_finseq\_1~X3~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_finseq\_1~X4~k2\_numbers){\unicdbdjdcd}\\
(((k3\_finseq\_1~X2=k3\_finseq\_1~X3){\unicdcdcdhd}(k3\_finseq\_1~X3=k3\_finseq\_1~\\
X4)){\unicdbdjdcd}(k8\_complsp2~(k9\_seq\_4~(k12\_seq\_4~X2~X0)~(k12\_seq\_4~X3~X1))~\\
X4=k3\_binop\_2~(k5\_binop\_2~X0~(k8\_complsp2~X2~X4))~(k5\_binop\_2~\\
X1~(k8\_complsp2~X3~X4))))))))\end{array}$$
\end{theorem}
\end{document}
