\documentclass{article}
\newtheorem{axiom}{Axiom}
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\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}
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\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{t72\_complsp2 (TMPJWnn6khHBMqEgk4S5cx5xYx1hhBrEDoD)}
\maketitle
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_numbers : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_complsp2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_seq\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_seq\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_seq\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_binop\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k30\_valued\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k45\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_membered : {{\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 $ k5\_numbers : {\iota}$ be given.
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~\\
X0~(k9\_seq\_4~X1~X2)=k3\_binop\_2~(k8\_complsp2~X0~X1)~(k8\_complsp2~\\
X0~X2)))))\end{array}
\label{hyp:ehhdbdpfdgpgngahmgdhahcd}
\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}((k3\_finseq\_1~X0=k3\_finseq\_1~X1){\unicdbdjdcd}(k8\_complsp2~\\
X0~(k11\_seq\_4~X1)=k1\_binop\_2~(k8\_complsp2~X0~X1))))\end{array}
\label{hyp:ehgdidpfdgpgngahmgdhahcd}
\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}((k3\_finseq\_1~X0=k3\_finseq\_1~X1){\unicdbdjdcd}(k8\_complsp2~\\
(k11\_seq\_4~X0)~X1=k1\_binop\_2~(k8\_complsp2~X0~X1))))\end{array}
\label{hyp:ehgdhdpfdgpgngahmgdhahcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_finseq\_1~\\
X0){\unicdcdcdhd}(v1\_valued\_0~X0)))){\unicdbdjdcd}(k3\_finseq\_1~(k30\_valued\_1~X0)=k3\_finseq\_1~\\
X0)\end{array}
\label{hyp:ehfdpfdgpgngahmgdhahcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xcmplx\_0~X0){\unicdcdcdhd}(v1\_xcmplx\_0~X1)){\unicdbdjdcd}(\\
k2\_xcmplx\_0~X0~(k4\_xcmplx\_0~X1)=k6\_xcmplx\_0~X0~X1)\end{array}
\label{hyp:dhahdgbdpfbgchjgehigng}
\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}(m1\_finseq\_1~\\
X1~k2\_numbers)){\unicdbdjdcd}(k9\_seq\_4~X0~X1=k1\_valued\_1~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfdhfgbhpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xcmplx\_0~X0){\unicdcdcdhd}(v1\_xcmplx\_0~X1)){\unicdbdjdcd}(\\
k4\_binop\_2~X0~X1=k6\_xcmplx\_0~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfcgjgogpgahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xcmplx\_0~X0){\unicdcdcdhd}(v1\_xcmplx\_0~X1)){\unicdbdjdcd}(\\
k3\_binop\_2~X0~X1=k2\_xcmplx\_0~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfcgjgogpgahpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{{k1\_binop\_2}~{X0}}={{k4\_xcmplx\_0}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfcgjgogpgahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_finseq\_1~X0~k2\_numbers){\unicdbdjdcd}(k11\_seq\_4~X0=k30\_valued\_1~\\
X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdbdpfdhfgbhpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_finseq\_1~X0~k2\_numbers){\unicdcdcdhd}(m1\_finseq\_1~\\
X1~k2\_numbers)){\unicdbdjdcd}(k10\_seq\_4~X0~X1=k45\_valued\_1~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdadpfdhfgbhpfed}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_membered}~{k2\_numbers}}\label{hyp:ggdgbdpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m2\_finseq\_1~X1~X0){\unicdbdjdcd}((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_finseq\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
X0)))))\end{array}
\label{hyp:egehpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_finseq\_1~X1~X0){\unicdbdjdcd}((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~X1)))\end{array}
\label{hyp:egehpfngbdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_finseq\_1~X0~k2\_numbers){\unicdcdcdhd}(m1\_finseq\_1~\\
X1~k2\_numbers)){\unicdbdjdcd}(m1\_subset\_1~(k8\_complsp2~X0~X1)~k2\_numbers)\end{array}
\label{hyp:egehpflgidpfdgpgngahmgdhahcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_finseq\_1~X0~k2\_numbers){\unicdbdjdcd}(m2\_finseq\_1~(k11\_seq\_4~\\
X0)~k2\_numbers)\end{array}
\label{hyp:egehpflgbdbdpfdhfgbhpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_valued\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_valued\_0~\\
X1))){\unicdbdjdcd}(k45\_valued\_1~X0~X1=k1\_valued\_1~X0~(k30\_valued\_1~X1)))\end{array}
\label{hyp:egjdpfghbgmgfhfgegpfbd}
\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}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_membered~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v1\_valued\_0~X2))\end{array}
\label{hyp:dgdgbdgdpfghbgmgfhfgegpfad}
\end{equation}
\begin{theorem}\label{thm:ehhdcdpfdgpgngahmgdhahcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_1~X0~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_1~\\
X1~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~k2\_numbers){\unicdbdjdcd}(((k3\_finseq\_1~\\
X0=k3\_finseq\_1~X1){\unicdcdcdhd}(k3\_finseq\_1~X1=k3\_finseq\_1~X2)){\unicdbdjdcd}(k8\_complsp2~\\
X0~(k10\_seq\_4~X1~X2)=k4\_binop\_2~(k8\_complsp2~X0~X1)~(k8\_complsp2~\\
X0~X2)))))\end{array}$$
\end{theorem}
\end{document}
