\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{l82\_descip\_1 (TMPRZna2sXkfbCgFg2WTyufdN5ocHRqwrHA)}
\maketitle
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ np\_\_16 : {\iota}$ be given.
Let $ k2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_descip\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ np\_\_4 : {\iota}$ be given.
Let $ np\_\_5 : {\iota}$ be given.
Let $ np\_\_6 : {\iota}$ be given.
Let $ np\_\_7 : {\iota}$ be given.
Let $ np\_\_8 : {\iota}$ be given.
Let $ np\_\_9 : {\iota}$ be given.
Let $ np\_\_10 : {\iota}$ be given.
Let $ np\_\_11 : {\iota}$ be given.
Let $ np\_\_12 : {\iota}$ be given.
Let $ np\_\_13 : {\iota}$ be given.
Let $ np\_\_14 : {\iota}$ be given.
Let $ np\_\_15 : {\iota}$ be given.
Let $ k1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ np\_\_0 : {\iota}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\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 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(\preoh v1\_xboole\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~X0~(k2\_finseq\_1~X0)){\unicdcdcdhd}((v1\_descip\_1~\\
X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~(k2\_finseq\_1~\\
X0))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}((\preoh r1\_xxreal\_0~X0~X2){\unicdbdjdcd}\\
((k1\_funct\_1~X1~X2=k1\_nat\_1~X2~np\_\_1){\unicdcdcdhd}(X2 \in k1\_relset\_1~X0~X1)))))\end{array}
\label{hyp:ehddedpfegfgdhdgjgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~X2)){\unicdbdjdcd}((X0 \in k9\_xtuple\_0~X1){\unicdbdjdcd}(k1\_funct\_1~\\
(k3\_relat\_1~X1~X2)~X0=k1\_funct\_1~X2~(k1\_funct\_1~X1~X0))))\end{array}
\label{hyp:ehbdddpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_9){\unicdcdcdhd}(m2\_subset\_1~np\_\_9~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_9~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_9~k1\_numbers))\end{array}
\label{hyp:dhahdgjdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_8){\unicdcdcdhd}(m2\_subset\_1~np\_\_8~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_8~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_8~k1\_numbers))\end{array}
\label{hyp:dhahdgidpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_7){\unicdcdcdhd}(m2\_subset\_1~np\_\_7~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_7~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_7~k1\_numbers))\end{array}
\label{hyp:dhahdghdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_6){\unicdcdcdhd}(m2\_subset\_1~np\_\_6~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_6~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_6~k1\_numbers))\end{array}
\label{hyp:dhahdggdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_5){\unicdcdcdhd}(m2\_subset\_1~np\_\_5~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_5~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_5~k1\_numbers))\end{array}
\label{hyp:dhahdgfdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_4){\unicdcdcdhd}(m2\_subset\_1~np\_\_4~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_4~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_4~k1\_numbers))\end{array}
\label{hyp:dhahdgedpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_3){\unicdcdcdhd}(m2\_subset\_1~np\_\_3~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_3~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_3~k1\_numbers))\end{array}
\label{hyp:dhahdgddpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_2){\unicdcdcdhd}(m2\_subset\_1~np\_\_2~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_2~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_2~k1\_numbers))\end{array}
\label{hyp:dhahdgcdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_16){\unicdcdcdhd}(m2\_subset\_1~np\_\_16~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_16~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_16~k1\_numbers))\end{array}
\label{hyp:dhahdgbdgdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{np\_\_16}}}}\label{hyp:dhahdgbdgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_15){\unicdcdcdhd}(m2\_subset\_1~np\_\_15~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_15~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_15~k1\_numbers))\end{array}
\label{hyp:dhahdgbdfdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_14){\unicdcdcdhd}(m2\_subset\_1~np\_\_14~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_14~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_14~k1\_numbers))\end{array}
\label{hyp:dhahdgbdedpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_13){\unicdcdcdhd}(m2\_subset\_1~np\_\_13~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_13~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_13~k1\_numbers))\end{array}
\label{hyp:dhahdgbdddpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_12){\unicdcdcdhd}(m2\_subset\_1~np\_\_12~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_12~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_12~k1\_numbers))\end{array}
\label{hyp:dhahdgbdcdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_11){\unicdcdcdhd}(m2\_subset\_1~np\_\_11~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_11~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_11~k1\_numbers))\end{array}
\label{hyp:dhahdgbdbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_10){\unicdcdcdhd}(m2\_subset\_1~np\_\_10~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_10~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_10~k1\_numbers))\end{array}
\label{hyp:dhahdgbdadpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(m2\_subset\_1~np\_\_0~k1\_numbers~k5\_numbers){\unicdcdcdhd}((m1\_subset\_1~np\_\_0~\\
k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_0~k1\_numbers))\end{array}
\label{hyp:dhahdgadpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{np\_\_0}}\label{hyp:dhahdgadpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{{{k2\_xcmplx\_0}~{np\_\_1}}~{np\_\_9}}={np\_\_10}}\label{hyp:chbhcffgbgmgbeegegpfpflgcdpfihdgngahmgihpfadpfpfchbdpfchjdpfchbdad}
\end{equation}
Assume the following.
\begin{equation}
{{{{k2\_xcmplx\_0}~{np\_\_1}}~{np\_\_8}}={np\_\_9}}\label{hyp:chbhcffgbgmgbeegegpfpflgcdpfihdgngahmgihpfadpfpfchbdpfchidpfchjd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k2\_xcmplx\_0}~{np\_\_1}}~{np\_\_7}}={np\_\_8}}\label{hyp:chbhcffgbgmgbeegegpfpflgcdpfihdgngahmgihpfadpfpfchbdpfchhdpfchid}
\end{equation}
Assume the following.
\begin{equation}
{{{{k2\_xcmplx\_0}~{np\_\_1}}~{np\_\_6}}={np\_\_7}}\label{hyp:chbhcffgbgmgbeegegpfpflgcdpfihdgngahmgihpfadpfpfchbdpfchgdpfchhd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k2\_xcmplx\_0}~{np\_\_1}}~{np\_\_5}}={np\_\_6}}\label{hyp:chbhcffgbgmgbeegegpfpflgcdpfihdgngahmgihpfadpfpfchbdpfchfdpfchgd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k2\_xcmplx\_0}~{np\_\_1}}~{np\_\_4}}={np\_\_5}}\label{hyp:chbhcffgbgmgbeegegpfpflgcdpfihdgngahmgihpfadpfpfchbdpfchedpfchfd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k2\_xcmplx\_0}~{np\_\_1}}~{np\_\_3}}={np\_\_4}}\label{hyp:chbhcffgbgmgbeegegpfpflgcdpfihdgngahmgihpfadpfpfchbdpfchddpfched}
\end{equation}
Assume the following.
\begin{equation}
{{{{k2\_xcmplx\_0}~{np\_\_1}}~{np\_\_2}}={np\_\_3}}\label{hyp:chbhcffgbgmgbeegegpfpflgcdpfihdgngahmgihpfadpfpfchbdpfchcdpfchdd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k2\_xcmplx\_0}~{np\_\_1}}~{np\_\_1}}={np\_\_2}}\label{hyp:chbhcffgbgmgbeegegpfpflgcdpfihdgngahmgihpfadpfpfchbdpfchbdpfchcd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k2\_xcmplx\_0}~{np\_\_1}}~{np\_\_15}}={np\_\_16}}\label{hyp:chbhcffgbgmgbeegegpfpflgcdpfihdgngahmgihpfadpfpfchbdpfchbdfdpfchbdgd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k2\_xcmplx\_0}~{np\_\_1}}~{np\_\_14}}={np\_\_15}}\label{hyp:chbhcffgbgmgbeegegpfpflgcdpfihdgngahmgihpfadpfpfchbdpfchbdedpfchbdfd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k2\_xcmplx\_0}~{np\_\_1}}~{np\_\_13}}={np\_\_14}}\label{hyp:chbhcffgbgmgbeegegpfpflgcdpfihdgngahmgihpfadpfpfchbdpfchbdddpfchbded}
\end{equation}
Assume the following.
\begin{equation}
{{{{k2\_xcmplx\_0}~{np\_\_1}}~{np\_\_12}}={np\_\_13}}\label{hyp:chbhcffgbgmgbeegegpfpflgcdpfihdgngahmgihpfadpfpfchbdpfchbdcdpfchbddd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k2\_xcmplx\_0}~{np\_\_1}}~{np\_\_11}}={np\_\_12}}\label{hyp:chbhcffgbgmgbeegegpfpflgcdpfihdgngahmgihpfadpfpfchbdpfchbdbdpfchbdcd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k2\_xcmplx\_0}~{np\_\_1}}~{np\_\_10}}={np\_\_11}}\label{hyp:chbhcffgbgmgbeegegpfpflgcdpfihdgngahmgihpfadpfpfchbdpfchbdadpfchbdbd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k2\_xcmplx\_0}~{np\_\_1}}~{np\_\_0}}={np\_\_1}}\label{hyp:chbhcffgbgmgbeegegpfpflgcdpfihdgngahmgihpfadpfpfchbdpfchadpfchbd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_16}}~{np\_\_9}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdgdpfchjd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_16}}~{np\_\_8}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdgdpfchid}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_16}}~{np\_\_7}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdgdpfchhd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_16}}~{np\_\_6}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdgdpfchgd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_16}}~{np\_\_5}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdgdpfchfd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_16}}~{np\_\_4}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdgdpfched}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_16}}~{np\_\_3}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdgdpfchdd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_16}}~{np\_\_2}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdgdpfchcd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_16}}~{np\_\_15}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdgdpfchbdfd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_16}}~{np\_\_14}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdgdpfchbded}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_16}}~{np\_\_13}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdgdpfchbddd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_16}}~{np\_\_12}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdgdpfchbdcd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_16}}~{np\_\_11}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdgdpfchbdbd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_16}}~{np\_\_10}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdgdpfchbdad}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_16}}~{np\_\_1}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdgdpfchbd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_16}}~{np\_\_0}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdgdpfchad}
\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 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v4\_relat\_1~X1~X0)){\unicdbdjdcd}(\\
k1\_relset\_1~X0~X1=k9\_xtuple\_0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1)))){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X2~X3))))){\unicdbdjdcd}(k1\_partfun1~X0~X1~X2~X3~X4~X5=k3\_relat\_1~X4~X5)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~k5\_numbers)){\unicdbdjdcd}\\
(k1\_nat\_1~X0~X1=k2\_xcmplx\_0~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{v1\_relat\_1}~{({{{k2\_zfmisc\_1}~{X0}}~{X1}})}}}}\label{hyp:ggdggdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_finseq\_2~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_2~\\
X2~X0~X1){\unicdbdjdcd}(m2\_finseq\_1~X2~X0))\end{array}
\label{hyp:egehpfngcdpfggjgogdhfgbhpfcd}
\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 .  (v7\_ordinal1~X0){\unicdbdjdcd}(m1\_finseq\_2~(k4\_finseq\_2~\\
X0~X1)~X1)\end{array}
\label{hyp:egehpflgedpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~k5\_numbers)){\unicdbdjdcd}\\
(k1\_nat\_1~X0~X1=k1\_nat\_1~X1~X0)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgbdpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}(v5\_relat\_1~X2~X1))\end{array}
\label{hyp:dgdgcdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_relat\_1~X1))\end{array}
\label{hyp:dgdgcdpfchfgmgbgehpfbd}
\end{equation}
\begin{theorem}\label{thm:mgidcdpfegfgdhdgjgahpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~np\_\_16~(k2\_finseq\_1~\\
np\_\_16)){\unicdcdcdhd}((v1\_descip\_1~X0~np\_\_16){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~np\_\_16~(k2\_finseq\_1~np\_\_16))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(\preoh v1\_xboole\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~X1){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~X1){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~X1){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~X1){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m1\_subset\_1~X7~X1){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~X1){\unicdbdjdcd}({\unicdcdadad} X9 .  \\
(m1\_subset\_1~X9~X1){\unicdbdjdcd}({\unicdcdadad} X10 .  (m1\_subset\_1~X10~X1){\unicdbdjdcd}({\unicdcdadad} X11 .  \\
(m1\_subset\_1~X11~X1){\unicdbdjdcd}({\unicdcdadad} X12 .  (m1\_subset\_1~X12~X1){\unicdbdjdcd}({\unicdcdadad} X13 .  \\
(m1\_subset\_1~X13~X1){\unicdbdjdcd}({\unicdcdadad} X14 .  (m1\_subset\_1~X14~X1){\unicdbdjdcd}({\unicdcdadad} X15 .  \\
(m1\_subset\_1~X15~X1){\unicdbdjdcd}({\unicdcdadad} X16 .  (m1\_subset\_1~X16~X1){\unicdbdjdcd}({\unicdcdadad} X17 .  \\
(m1\_subset\_1~X17~X1){\unicdbdjdcd}({\unicdcdadad} X18 .  (m2\_finseq\_2~X18~X1~(k4\_finseq\_2~\\
np\_\_16~X1)){\unicdbdjdcd}(((k1\_funct\_1~X18~np\_\_1=X2){\unicdcdcdhd}((k1\_funct\_1~X18~np\_\_2=\\
X3){\unicdcdcdhd}((k1\_funct\_1~X18~np\_\_3=X4){\unicdcdcdhd}((k1\_funct\_1~X18~np\_\_4=X5){\unicdcdcdhd}(\\
(k1\_funct\_1~X18~np\_\_5=X6){\unicdcdcdhd}((k1\_funct\_1~X18~np\_\_6=X7){\unicdcdcdhd}((k1\_funct\_1~\\
X18~np\_\_7=X8){\unicdcdcdhd}((k1\_funct\_1~X18~np\_\_8=X9){\unicdcdcdhd}((k1\_funct\_1~X18~np\_\_9=\\
X10){\unicdcdcdhd}((k1\_funct\_1~X18~np\_\_10=X11){\unicdcdcdhd}((k1\_funct\_1~X18~np\_\_11=X12){\unicdcdcdhd}\\
((k1\_funct\_1~X18~np\_\_12=X13){\unicdcdcdhd}((k1\_funct\_1~X18~np\_\_13=X14){\unicdcdcdhd}(\\
(k1\_funct\_1~X18~np\_\_14=X15){\unicdcdcdhd}((k1\_funct\_1~X18~np\_\_15=X16){\unicdcdcdhd}(k1\_funct\_1~\\
X18~np\_\_16=X17)))))))))))))))){\unicdbdjdcd}((k1\_funct\_1~(k1\_partfun1~np\_\_16~\\
(k2\_finseq\_1~np\_\_16)~k5\_numbers~X1~X0~X18)~k6\_numbers=X2){\unicdcdcdhd}((k1\_funct\_1~\\
(k1\_partfun1~np\_\_16~(k2\_finseq\_1~np\_\_16)~k5\_numbers~X1~X0~X18)~\\
np\_\_1=X3){\unicdcdcdhd}((k1\_funct\_1~(k1\_partfun1~np\_\_16~(k2\_finseq\_1~np\_\_16)~\\
k5\_numbers~X1~X0~X18)~np\_\_2=X4){\unicdcdcdhd}((k1\_funct\_1~(k1\_partfun1~np\_\_16~\\
(k2\_finseq\_1~np\_\_16)~k5\_numbers~X1~X0~X18)~np\_\_3=X5){\unicdcdcdhd}((k1\_funct\_1~\\
(k1\_partfun1~np\_\_16~(k2\_finseq\_1~np\_\_16)~k5\_numbers~X1~X0~X18)~\\
np\_\_4=X6){\unicdcdcdhd}((k1\_funct\_1~(k1\_partfun1~np\_\_16~(k2\_finseq\_1~np\_\_16)~\\
k5\_numbers~X1~X0~X18)~np\_\_5=X7){\unicdcdcdhd}((k1\_funct\_1~(k1\_partfun1~np\_\_16~\\
(k2\_finseq\_1~np\_\_16)~k5\_numbers~X1~X0~X18)~np\_\_6=X8){\unicdcdcdhd}((k1\_funct\_1~\\
(k1\_partfun1~np\_\_16~(k2\_finseq\_1~np\_\_16)~k5\_numbers~X1~X0~X18)~\\
np\_\_7=X9){\unicdcdcdhd}((k1\_funct\_1~(k1\_partfun1~np\_\_16~(k2\_finseq\_1~np\_\_16)~\\
k5\_numbers~X1~X0~X18)~np\_\_8=X10){\unicdcdcdhd}((k1\_funct\_1~(k1\_partfun1~np\_\_16~\\
(k2\_finseq\_1~np\_\_16)~k5\_numbers~X1~X0~X18)~np\_\_9=X11){\unicdcdcdhd}((k1\_funct\_1~\\
(k1\_partfun1~np\_\_16~(k2\_finseq\_1~np\_\_16)~k5\_numbers~X1~X0~X18)~\\
np\_\_10=X12){\unicdcdcdhd}((k1\_funct\_1~(k1\_partfun1~np\_\_16~(k2\_finseq\_1~np\_\_16)~\\
k5\_numbers~X1~X0~X18)~np\_\_11=X13){\unicdcdcdhd}((k1\_funct\_1~(k1\_partfun1~np\_\_16~\\
(k2\_finseq\_1~np\_\_16)~k5\_numbers~X1~X0~X18)~np\_\_12=X14){\unicdcdcdhd}((k1\_funct\_1~\\
(k1\_partfun1~np\_\_16~(k2\_finseq\_1~np\_\_16)~k5\_numbers~X1~X0~X18)~\\
np\_\_13=X15){\unicdcdcdhd}((k1\_funct\_1~(k1\_partfun1~np\_\_16~(k2\_finseq\_1~np\_\_16)~\\
k5\_numbers~X1~X0~X18)~np\_\_14=X16){\unicdcdcdhd}(k1\_funct\_1~(k1\_partfun1~np\_\_16~\\
(k2\_finseq\_1~np\_\_16)~k5\_numbers~X1~X0~X18)~np\_\_15=X17)))))))))))))))))))))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
