\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{t19\_descip\_1 (TMKYiGW47TeNYHSwYoX4uDMYFZNLZJCsa58)}
\maketitle
Let $ k2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_16 : {\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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ 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 $ k5\_numbers : {\iota}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v6\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\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}
\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}
{{{{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}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\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 .  ((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}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}(\preoh \\
(r1\_xxreal\_0~X0~X1){\unicdcdcdhd}((r1\_xxreal\_0~X1~(k1\_nat\_1~X0~np\_\_15)){\unicdcdcdhd}((\\
X1{\unicdcdgdad}X0){\unicdcdcdhd}((X1{\unicdcdgdad}k1\_nat\_1~X0~np\_\_1){\unicdcdcdhd}((X1{\unicdcdgdad}k1\_nat\_1~X0~np\_\_2){\unicdcdcdhd}((X1{\unicdcdgdad}\\
k1\_nat\_1~X0~np\_\_3){\unicdcdcdhd}((X1{\unicdcdgdad}k1\_nat\_1~X0~np\_\_4){\unicdcdcdhd}((X1{\unicdcdgdad}k1\_nat\_1~X0~np\_\_5){\unicdcdcdhd}\\
((X1{\unicdcdgdad}k1\_nat\_1~X0~np\_\_6){\unicdcdcdhd}((X1{\unicdcdgdad}k1\_nat\_1~X0~np\_\_7){\unicdcdcdhd}((X1{\unicdcdgdad}k1\_nat\_1~\\
X0~np\_\_8){\unicdcdcdhd}((X1{\unicdcdgdad}k1\_nat\_1~X0~np\_\_9){\unicdcdcdhd}((X1{\unicdcdgdad}k1\_nat\_1~X0~np\_\_10){\unicdcdcdhd}(\\
(X1{\unicdcdgdad}k1\_nat\_1~X0~np\_\_11){\unicdcdcdhd}((X1{\unicdcdgdad}k1\_nat\_1~X0~np\_\_12){\unicdcdcdhd}((X1{\unicdcdgdad}k1\_nat\_1~\\
X0~np\_\_13){\unicdcdcdhd}((X1{\unicdcdgdad}k1\_nat\_1~X0~np\_\_14){\unicdcdcdhd}(X1{\unicdcdgdad}k1\_nat\_1~X0~np\_\_15)))))))))))))))))))\end{array}
\label{hyp:mgcdfdpfegfgdhdgjgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v6\_membered}~{k4\_ordinal1}}\label{hyp:ggdggdpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}(m1\_subset\_1~(k2\_finseq\_1~X0)~(k1\_zfmisc\_1~\\
k5\_numbers))\end{array}
\label{hyp:egehpflgcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}(k1\_finseq\_1~X0=ReplSep~(toset~(\\
{\uniddcgcg} X1 : \iota .  m2\_subset\_1~X1~k1\_numbers~k5\_numbers))~({\uniddcgcg} X1 : \iota .  \\
(r1\_xxreal\_0~np\_\_1~X1){\unicdcdcdhd}(r1\_xxreal\_0~X1~X0))~({\uniddcgcg} X1 : \iota .  X1))\end{array}
\label{hyp:egbdpfggjgogdhfgbhpfbd}
\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 .  (v6\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v6\_membered~X1))\end{array}
\label{hyp:dgdgcdedpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v6\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v7\_ordinal1~X1))\end{array}
\label{hyp:dgdgbdhdpfngfgngcgfgchfgeg}
\end{equation}
\begin{theorem}\label{thm:ehbdjdpfegfgdhdgjgahpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  \preoh (X0 \in k2\_finseq\_1~np\_\_16){\unicdcdcdhd}((X0{\unicdcdgdad}np\_\_1){\unicdcdcdhd}((X0{\unicdcdgdad}np\_\_2){\unicdcdcdhd}\\
((X0{\unicdcdgdad}np\_\_3){\unicdcdcdhd}((X0{\unicdcdgdad}np\_\_4){\unicdcdcdhd}((X0{\unicdcdgdad}np\_\_5){\unicdcdcdhd}((X0{\unicdcdgdad}np\_\_6){\unicdcdcdhd}((X0{\unicdcdgdad}np\_\_7){\unicdcdcdhd}\\
((X0{\unicdcdgdad}np\_\_8){\unicdcdcdhd}((X0{\unicdcdgdad}np\_\_9){\unicdcdcdhd}((X0{\unicdcdgdad}np\_\_10){\unicdcdcdhd}((X0{\unicdcdgdad}np\_\_11){\unicdcdcdhd}((X0{\unicdcdgdad}\\
np\_\_12){\unicdcdcdhd}((X0{\unicdcdgdad}np\_\_13){\unicdcdcdhd}((X0{\unicdcdgdad}np\_\_14){\unicdcdcdhd}((X0{\unicdcdgdad}np\_\_15){\unicdcdcdhd}(X0{\unicdcdgdad}np\_\_16))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
