\documentclass{article}
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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}
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\newcommand\unicdbdjded{\Leftrightarrow}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t57\_finseqop (TMUhPmiKLLbojCpTgQczbhc1dzPYi5XBJAk)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_card\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_finseq\_1 : {{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_setwiseo : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k3\_finseqop : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k4\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ r2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k10\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k5\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~\\
X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k2\_zfmisc\_1~X1~X1)~X1){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X1~X1)~X1))))){\unicdbdjdcd}((v1\_setwiseo~X3~X1){\unicdbdjdcd}\\
(r2\_funct\_2~X0~X1~(k10\_funcop\_1~X1~X0~X3~(k4\_binop\_1~X1~X3)~X2)~X2)))))\end{array}
\label{hyp:ehededpfggjgogdhfgbhpgah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}((r2\_relset\_1~X0~X1~X2~X3){\unicdbdjded}(X2=X3))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((v1\_funct\_1~X2){\unicdcdcdhd}\\
((v1\_funct\_2~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1))))){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~X0~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)))))){\unicdbdjdcd}((r2\_funct\_2~X0~X1~X2~\\
X3){\unicdbdjded}(X2=X3))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfggfhogdgehpfcd}
\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}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(\\
((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k2\_zfmisc\_1~X0~X1)~X2){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)~X2))))){\unicdcdcdhd}((m1\_subset\_1~\\
X4~X0){\unicdcdcdhd}(m1\_finseq\_1~X5~X1)))))){\unicdbdjdcd}(k3\_finseqop~X0~X1~X2~X3~X4~X5=k5\_funcop\_1~\\
X3~X4~X5)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfggjgogdhfgbhpgah}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{{k2\_finseq\_1}~{X0}}={{k1\_finseq\_1}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~\\
X0))))){\unicdcdcdhd}((m1\_subset\_1~X3~X0){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~\\
X4~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X0)))))))){\unicdbdjdcd}\\
(k10\_funcop\_1~X0~X1~X2~X3~X4=k5\_funcop\_1~X2~X3~X4)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdadpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((v3\_card\_1~X2~X1){\unicdcdcdhd}(m2\_finseq\_1~X2~X0)){\unicdbdjdcd}((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_finseq\_1~X1)~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_finseq\_1~X1)~X0)))))))\end{array}
\label{hyp:mgcdhdpfggjgogdhfgbhpgah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~X0){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~(k2\_zfmisc\_1~X0~\\
X1)~X2){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1)~X2))))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v3\_card\_1~X5~k6\_numbers){\unicdcdcdhd}(m2\_finseq\_1~\\
X5~X1)){\unicdbdjdcd}(r2\_relset\_1~k5\_numbers~X2~(k3\_finseqop~X0~X1~X2~X4~X3~X5)~\\
(k6\_finseq\_1~X2)))))))\end{array}
\label{hyp:mgbdbdpfggjgogdhfgbhpgah}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v1\_xboole\_0}~{({{k6\_finseq\_1}~{X0}})}}}\label{hyp:ggdgfdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(\preoh v1\_xboole\_0~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(k1\_finseq\_1~X0))\end{array}
\label{hyp:ggdgcdddpfggjgogdhfgbhpfbd}
\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 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_zfmisc\_1~\\
X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0)~X0))))){\unicdbdjdcd}(m1\_subset\_1~(k4\_binop\_1~X0~X1)~X0)\end{array}
\label{hyp:egehpflgedpfcgjgogpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~\\
X0))))){\unicdcdcdhd}((m1\_subset\_1~X3~X0){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~\\
X4~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X0)))))))){\unicdbdjdcd}\\
((v1\_funct\_1~(k10\_funcop\_1~X0~X1~X2~X3~X4)){\unicdcdcdhd}((v1\_funct\_2~(k10\_funcop\_1~\\
X0~X1~X2~X3~X4)~X1~X0){\unicdcdcdhd}(m1\_subset\_1~(k10\_funcop\_1~X0~X1~X2~X3~X4)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X1~X0)))))\end{array}
\label{hyp:egehpflgbdadpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{v3\_card\_1}~{X0}}~{k1\_xboole\_0}})}{\unicdbdjdcd}{({{v1\_xboole\_0}~{X0}})}}}\label{hyp:dgdghdpfdgbgchegpfbd}
\end{equation}
\begin{theorem}\label{thm:ehfdhdpfggjgogdhfgbhpgah}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((v3\_card\_1~X2~X1){\unicdcdcdhd}(m2\_finseq\_1~X2~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdbdjdcd}((v1\_setwiseo~\\
X3~X0){\unicdbdjdcd}(r2\_relset\_1~k5\_numbers~X0~(k3\_finseqop~X0~X0~X0~X3~(k4\_binop\_1~\\
X0~X3)~X2)~X2)))))\end{array}$$
\end{theorem}
\end{document}
