\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{t79\_scmpds\_2 (TMWN6o5MCGUZcv9jGt5SqxFW9YhAgQFwPCJ)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_scmpds\_2 : {\iota}$ be given.
Let $ k3\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v1\_int\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_scmpds\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_ami\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_scmpds\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_scmpds\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_scmpds\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_scmpds\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_scmpds\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k8\_scmpds\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_scmpds\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k11\_scmpds\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k12\_scmpds\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k13\_scmpds\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k14\_scmpds\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k15\_scmpds\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k16\_scmpds\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_compos\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_13 : {\iota}$ be given.
Let $ np\_\_12 : {\iota}$ be given.
Let $ np\_\_11 : {\iota}$ be given.
Let $ np\_\_10 : {\iota}$ be given.
Let $ np\_\_9 : {\iota}$ be given.
Let $ np\_\_8 : {\iota}$ be given.
Let $ np\_\_7 : {\iota}$ be given.
Let $ np\_\_6 : {\iota}$ be given.
Let $ np\_\_5 : {\iota}$ be given.
Let $ np\_\_4 : {\iota}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ np\_\_14 : {\iota}$ be given.
Let $ k2\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_ami\_3 : {\iota}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_numbers : {\iota}$ be given.
Let $ k9\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_ami\_2 : {\iota}$ be given.
Let $ k2\_ami\_2 : {\iota}$ be given.
Let $ k12\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_15 : {\iota}$ be given.
Let $ k3\_scmpds\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k7\_finseq\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdbdjdcd}(\preoh (k2\_compos\_0~\\
(u1\_compos\_1~k1\_scmpds\_2)~X0=np\_\_13){\unicdcdcdhd}({\unicdcdadad} X1 .  ((v1\_ami\_2~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_ami\_2~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (v1\_int\_1~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v1\_int\_1~X4){\unicdbdjdcd}(X0{\unicdcdgdad}k16\_scmpds\_2~\\
X1~X2~X3~X4))))))\end{array}
\label{hyp:ehddjdpfdhdgngahegdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdbdjdcd}(\preoh (k2\_compos\_0~\\
(u1\_compos\_1~k1\_scmpds\_2)~X0=np\_\_12){\unicdcdcdhd}({\unicdcdadad} X1 .  ((v1\_ami\_2~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_ami\_2~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (v1\_int\_1~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v1\_int\_1~X4){\unicdbdjdcd}(X0{\unicdcdgdad}k15\_scmpds\_2~\\
X1~X2~X3~X4))))))\end{array}
\label{hyp:ehddidpfdhdgngahegdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdbdjdcd}(\preoh (k2\_compos\_0~\\
(u1\_compos\_1~k1\_scmpds\_2)~X0=np\_\_11){\unicdcdcdhd}({\unicdcdadad} X1 .  ((v1\_ami\_2~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_ami\_2~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (v1\_int\_1~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v1\_int\_1~X4){\unicdbdjdcd}(X0{\unicdcdgdad}k14\_scmpds\_2~\\
X1~X2~X3~X4))))))\end{array}
\label{hyp:ehddhdpfdhdgngahegdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdbdjdcd}(\preoh (k2\_compos\_0~\\
(u1\_compos\_1~k1\_scmpds\_2)~X0=np\_\_10){\unicdcdcdhd}({\unicdcdadad} X1 .  ((v1\_ami\_2~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_ami\_2~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (v1\_int\_1~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v1\_int\_1~X4){\unicdbdjdcd}(X0{\unicdcdgdad}k13\_scmpds\_2~\\
X1~X2~X3~X4))))))\end{array}
\label{hyp:ehddgdpfdhdgngahegdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdbdjdcd}(\preoh (k2\_compos\_0~\\
(u1\_compos\_1~k1\_scmpds\_2)~X0=np\_\_9){\unicdcdcdhd}({\unicdcdadad} X1 .  ((v1\_ami\_2~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_ami\_2~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (v1\_int\_1~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v1\_int\_1~X4){\unicdbdjdcd}(X0{\unicdcdgdad}k12\_scmpds\_2~\\
X1~X2~X3~X4))))))\end{array}
\label{hyp:ehddfdpfdhdgngahegdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdbdjdcd}(\preoh (k2\_compos\_0~\\
(u1\_compos\_1~k1\_scmpds\_2)~X0=np\_\_8){\unicdcdcdhd}({\unicdcdadad} X1 .  ((v1\_ami\_2~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_int\_1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_int\_1~X3){\unicdbdjdcd}(X0{\unicdcdgdad}k11\_scmpds\_2~X1~\\
X2~X3)))))\end{array}
\label{hyp:ehddedpfdhdgngahegdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdbdjdcd}(\preoh (k2\_compos\_0~\\
(u1\_compos\_1~k1\_scmpds\_2)~X0=np\_\_7){\unicdcdcdhd}({\unicdcdadad} X1 .  ((v1\_ami\_2~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_int\_1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_int\_1~X3){\unicdbdjdcd}(X0{\unicdcdgdad}k10\_scmpds\_2~X1~\\
X2~X3)))))\end{array}
\label{hyp:ehddddpfdhdgngahegdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdbdjdcd}(\preoh (k2\_compos\_0~\\
(u1\_compos\_1~k1\_scmpds\_2)~X0=np\_\_6){\unicdcdcdhd}({\unicdcdadad} X1 .  ((v1\_ami\_2~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_int\_1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_int\_1~X3){\unicdbdjdcd}(X0{\unicdcdgdad}k9\_scmpds\_2~X1~X2~\\
X3)))))\end{array}
\label{hyp:ehddcdpfdhdgngahegdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdbdjdcd}(\preoh (k2\_compos\_0~\\
(u1\_compos\_1~k1\_scmpds\_2)~X0=np\_\_5){\unicdcdcdhd}({\unicdcdadad} X1 .  ((v1\_ami\_2~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_int\_1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_int\_1~X3){\unicdbdjdcd}(X0{\unicdcdgdad}k8\_scmpds\_2~X1~X2~\\
X3)))))\end{array}
\label{hyp:ehddbdpfdhdgngahegdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdbdjdcd}(\preoh (k2\_compos\_0~\\
(u1\_compos\_1~k1\_scmpds\_2)~X0=np\_\_4){\unicdcdcdhd}({\unicdcdadad} X1 .  ((v1\_ami\_2~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_int\_1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_int\_1~X3){\unicdbdjdcd}(X0{\unicdcdgdad}k7\_scmpds\_2~X1~X2~\\
X3)))))\end{array}
\label{hyp:ehddadpfdhdgngahegdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdbdjdcd}(\preoh (k2\_compos\_0~\\
(u1\_compos\_1~k1\_scmpds\_2)~X0=np\_\_3){\unicdcdcdhd}({\unicdcdadad} X1 .  ((v1\_ami\_2~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_int\_1~X2){\unicdbdjdcd}(X0{\unicdcdgdad}k6\_scmpds\_2~X1~X2))))\end{array}
\label{hyp:ehcdjdpfdhdgngahegdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdbdjdcd}(\preoh (k2\_compos\_0~\\
(u1\_compos\_1~k1\_scmpds\_2)~X0=np\_\_2){\unicdcdcdhd}({\unicdcdadad} X1 .  ((v1\_ami\_2~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_int\_1~X2){\unicdbdjdcd}(X0{\unicdcdgdad}k5\_scmpds\_2~X1~X2))))\end{array}
\label{hyp:ehcdidpfdhdgngahegdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdbdjdcd}(\preoh (k2\_compos\_0~\\
(u1\_compos\_1~k1\_scmpds\_2)~X0=np\_\_1){\unicdcdcdhd}({\unicdcdadad} X1 .  ((v1\_ami\_2~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}(X0{\unicdcdgdad}k4\_scmpds\_2~\\
X1)))\end{array}
\label{hyp:ehcdhdpfdhdgngahegdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdbdjdcd}(\preoh (k2\_compos\_0~\\
(u1\_compos\_1~k1\_scmpds\_2)~X0=np\_\_14){\unicdcdcdhd}({\unicdcdadad} X1 .  (v1\_int\_1~\\
X1){\unicdbdjdcd}(X0{\unicdcdgdad}k3\_scmpds\_2~X1)))\end{array}
\label{hyp:ehcdgdpfdhdgngahegdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{{k2\_compos\_1}~{k1\_ami\_3}}={{{{k3\_xtuple\_0}~{k6\_numbers}}~{k1\_xboole\_0}}~{k1\_xboole\_0}}}\label{hyp:ehcdgdpfbgngjgpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdbdjdcd}(\preoh (\preoh X0 \in \\
k1\_tarski~(k3\_xtuple\_0~k6\_numbers~k1\_xboole\_0~k1\_xboole\_0)){\unicdcdcdhd}\\
((\preoh X0 \in ReplSep~(toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~X1~k4\_numbers))~\\
({\uniddcgcg} X1 : \iota .  True)~({\uniddcgcg} X1 : \iota .  k3\_xtuple\_0~np\_\_14~k1\_xboole\_0~\\
(k9\_finseq\_1~X1))){\unicdcdcdhd}((\preoh X0 \in ReplSep~(toset~({\uniddcgcg} X1 : \iota .  m2\_subset\_1~\\
X1~k1\_ami\_2~k2\_ami\_2))~({\uniddcgcg} X1 : \iota .  True)~({\uniddcgcg} X1 : \iota .  k3\_xtuple\_0~\\
np\_\_1~k1\_xboole\_0~(k12\_finseq\_1~k2\_ami\_2~X1))){\unicdcdcdhd}((\preoh X0 \in ReplSep3~\\
(toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~X1~(k7\_card\_1~np\_\_15)))~({\uniddcgcg} X1 : \\
\iota .  toset~({\uniddcgcg} X2 : \iota .  m2\_subset\_1~X2~k1\_ami\_2~k2\_ami\_2))~({\uniddcgcg} X1 : \\
\iota .  {\uniddcgcg} X2 : \iota .  toset~({\uniddcgcg} X3 : \iota .  m1\_subset\_1~X3~k4\_numbers))~\\
({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  X1 \in k2\_tarski~np\_\_2~np\_\_3)~\\
({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  k3\_xtuple\_0~X1~k1\_xboole\_0~\\
(k3\_scmpds\_1~X2~X3))){\unicdcdcdhd}((\preoh X0 \in ReplSep4~(toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~\\
X1~(k7\_card\_1~np\_\_15)))~({\uniddcgcg} X1 : \iota .  toset~({\uniddcgcg} X2 : \iota .  m2\_subset\_1~\\
X2~k1\_ami\_2~k2\_ami\_2))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  toset~({\uniddcgcg} X3 : \\
\iota .  m1\_subset\_1~X3~k4\_numbers))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \\
\iota .  toset~({\uniddcgcg} X4 : \iota .  m1\_subset\_1~X4~k4\_numbers))~({\uniddcgcg} X1 : \iota .  \\
{\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  {\uniddcgcg} X4 : \iota .  X1 \in k3\_enumset1~np\_\_4~np\_\_5~\\
np\_\_6~np\_\_7~np\_\_8)~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  {\uniddcgcg} X4 : \\
\iota .  k3\_xtuple\_0~X1~k1\_xboole\_0~(k11\_finseq\_1~X2~X3~X4))){\unicdcdcdhd}(\preoh X0 \in \\
ReplSep5~(toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~X1~(k7\_card\_1~np\_\_15)))~\\
({\uniddcgcg} X1 : \iota .  toset~({\uniddcgcg} X2 : \iota .  m2\_subset\_1~X2~k1\_ami\_2~k2\_ami\_2))~\\
({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  toset~({\uniddcgcg} X3 : \iota .  m2\_subset\_1~X3~k1\_ami\_2~\\
k2\_ami\_2))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  toset~({\uniddcgcg} X4 : \\
\iota .  m1\_subset\_1~X4~k4\_numbers))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \\
\iota .  {\uniddcgcg} X4 : \iota .  toset~({\uniddcgcg} X5 : \iota .  m1\_subset\_1~X5~k4\_numbers))~\\
({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  {\uniddcgcg} X4 : \iota .  {\uniddcgcg} X5 : \iota .  \\
X1 \in k3\_enumset1~np\_\_9~np\_\_10~np\_\_11~np\_\_12~np\_\_13)~({\uniddcgcg} X1 : \iota .  \\
{\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  {\uniddcgcg} X4 : \iota .  {\uniddcgcg} X5 : \iota .  k3\_xtuple\_0~\\
X1~k1\_xboole\_0~(k7\_finseq\_4~X2~X3~X4~X5))))))))\end{array}
\label{hyp:mgidpfdhdgngahegdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdbdjdcd}(\preoh (X0 \in \\
ReplSep5~(toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~X1~(k7\_card\_1~np\_\_15)))~\\
({\uniddcgcg} X1 : \iota .  toset~({\uniddcgcg} X2 : \iota .  m2\_subset\_1~X2~k1\_ami\_2~k2\_ami\_2))~\\
({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  toset~({\uniddcgcg} X3 : \iota .  m2\_subset\_1~X3~k1\_ami\_2~\\
k2\_ami\_2))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  toset~({\uniddcgcg} X4 : \\
\iota .  m1\_subset\_1~X4~k4\_numbers))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \\
\iota .  {\uniddcgcg} X4 : \iota .  toset~({\uniddcgcg} X5 : \iota .  m1\_subset\_1~X5~k4\_numbers))~\\
({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  {\uniddcgcg} X4 : \iota .  {\uniddcgcg} X5 : \iota .  \\
X1 \in k3\_enumset1~np\_\_9~np\_\_10~np\_\_11~np\_\_12~np\_\_13)~({\uniddcgcg} X1 : \iota .  \\
{\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  {\uniddcgcg} X4 : \iota .  {\uniddcgcg} X5 : \iota .  k3\_xtuple\_0~\\
X1~k1\_xboole\_0~(k7\_finseq\_4~X2~X3~X4~X5))){\unicdcdcdhd}((k2\_compos\_0~(u1\_compos\_1~\\
k1\_scmpds\_2)~X0{\unicdcdgdad}np\_\_9){\unicdcdcdhd}((k2\_compos\_0~(u1\_compos\_1~k1\_scmpds\_2)~\\
X0{\unicdcdgdad}np\_\_10){\unicdcdcdhd}((k2\_compos\_0~(u1\_compos\_1~k1\_scmpds\_2)~X0{\unicdcdgdad}np\_\_11){\unicdcdcdhd}\\
((k2\_compos\_0~(u1\_compos\_1~k1\_scmpds\_2)~X0{\unicdcdgdad}np\_\_12){\unicdcdcdhd}(k2\_compos\_0~\\
(u1\_compos\_1~k1\_scmpds\_2)~X0{\unicdcdgdad}np\_\_13))))))\end{array}
\label{hyp:mgedidpfdhdgngahegdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdbdjdcd}(\preoh (X0 \in \\
ReplSep4~(toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~X1~(k7\_card\_1~np\_\_15)))~\\
({\uniddcgcg} X1 : \iota .  toset~({\uniddcgcg} X2 : \iota .  m2\_subset\_1~X2~k1\_ami\_2~k2\_ami\_2))~\\
({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  toset~({\uniddcgcg} X3 : \iota .  m1\_subset\_1~X3~k4\_numbers))~\\
({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  toset~({\uniddcgcg} X4 : \iota .  m1\_subset\_1~\\
X4~k4\_numbers))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  {\uniddcgcg} X4 : \\
\iota .  X1 \in k3\_enumset1~np\_\_4~np\_\_5~np\_\_6~np\_\_7~np\_\_8)~({\uniddcgcg} X1 : \iota .  \\
{\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  {\uniddcgcg} X4 : \iota .  k3\_xtuple\_0~X1~k1\_xboole\_0~\\
(k11\_finseq\_1~X2~X3~X4))){\unicdcdcdhd}((k2\_compos\_0~(u1\_compos\_1~k1\_scmpds\_2)~\\
X0{\unicdcdgdad}np\_\_4){\unicdcdcdhd}((k2\_compos\_0~(u1\_compos\_1~k1\_scmpds\_2)~X0{\unicdcdgdad}np\_\_5){\unicdcdcdhd}\\
((k2\_compos\_0~(u1\_compos\_1~k1\_scmpds\_2)~X0{\unicdcdgdad}np\_\_6){\unicdcdcdhd}((k2\_compos\_0~\\
(u1\_compos\_1~k1\_scmpds\_2)~X0{\unicdcdgdad}np\_\_7){\unicdcdcdhd}(k2\_compos\_0~(u1\_compos\_1~\\
k1\_scmpds\_2)~X0{\unicdcdgdad}np\_\_8))))))\end{array}
\label{hyp:mgedhdpfdhdgngahegdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdbdjdcd}(\preoh (X0 \in \\
ReplSep3~(toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~X1~(k7\_card\_1~np\_\_15)))~\\
({\uniddcgcg} X1 : \iota .  toset~({\uniddcgcg} X2 : \iota .  m2\_subset\_1~X2~k1\_ami\_2~k2\_ami\_2))~\\
({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  toset~({\uniddcgcg} X3 : \iota .  m1\_subset\_1~X3~k4\_numbers))~\\
({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  X1 \in k2\_tarski~np\_\_2~np\_\_3)~\\
({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  k3\_xtuple\_0~X1~k1\_xboole\_0~\\
(k3\_scmpds\_1~X2~X3))){\unicdcdcdhd}((k2\_compos\_0~(u1\_compos\_1~k1\_scmpds\_2)~\\
X0{\unicdcdgdad}np\_\_2){\unicdcdcdhd}(k2\_compos\_0~(u1\_compos\_1~k1\_scmpds\_2)~X0{\unicdcdgdad}np\_\_3)))\end{array}
\label{hyp:mgedgdpfdhdgngahegdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdbdjdcd}((X0 \in \\
ReplSep~(toset~({\uniddcgcg} X1 : \iota .  m2\_subset\_1~X1~k1\_ami\_2~k2\_ami\_2))~\\
({\uniddcgcg} X1 : \iota .  True)~({\uniddcgcg} X1 : \iota .  k3\_xtuple\_0~np\_\_1~k1\_xboole\_0~\\
(k12\_finseq\_1~k2\_ami\_2~X1))){\unicdbdjdcd}(k2\_compos\_0~(u1\_compos\_1~k1\_scmpds\_2)~\\
X0=np\_\_1))\end{array}
\label{hyp:mgedfdpfdhdgngahegdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdbdjdcd}((X0 \in \\
ReplSep~(toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~X1~k4\_numbers))~({\uniddcgcg} X1 : \\
\iota .  True)~({\uniddcgcg} X1 : \iota .  k3\_xtuple\_0~np\_\_14~k1\_xboole\_0~(k9\_finseq\_1~\\
X1))){\unicdbdjdcd}(k2\_compos\_0~(u1\_compos\_1~k1\_scmpds\_2)~X0=np\_\_14))\end{array}
\label{hyp:mgededpfdhdgngahegdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k3\_xtuple\_0~X0~X1~X2=k4\_tarski~\\
(k4\_tarski~X0~X1)~X2\end{array}
\label{hyp:egedpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X1=k1\_tarski~X0){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}\\
(X2=X0))\end{array}
\label{hyp:egbdpfehbgchdhlgjg}
\end{equation}
\begin{theorem}\label{thm:ehhdjdpfdhdgngahegdhpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  \preoh (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}((X0{\unicdcdgdad}\\
k3\_xtuple\_0~k6\_numbers~k1\_xboole\_0~k1\_xboole\_0){\unicdcdcdhd}(({\unicdcdadad} X1 .  \\
(v1\_int\_1~X1){\unicdbdjdcd}(X0{\unicdcdgdad}k3\_scmpds\_2~X1)){\unicdcdcdhd}(({\unicdcdadad} X1 .  ((v1\_ami\_2~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}(X0{\unicdcdgdad}k4\_scmpds\_2~\\
X1)){\unicdcdcdhd}(({\unicdcdadad} X1 .  ((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~\\
k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_int\_1~X2){\unicdbdjdcd}(X0{\unicdcdgdad}k6\_scmpds\_2~X1~\\
X2))){\unicdcdcdhd}(({\unicdcdadad} X1 .  ((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~\\
k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_int\_1~X2){\unicdbdjdcd}(X0{\unicdcdgdad}k5\_scmpds\_2~X1~\\
X2))){\unicdcdcdhd}(({\unicdcdadad} X1 .  ((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~\\
k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_int\_1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_int\_1~\\
X3){\unicdbdjdcd}(X0{\unicdcdgdad}k10\_scmpds\_2~X1~X2~X3)))){\unicdcdcdhd}(({\unicdcdadad} X1 .  ((v1\_ami\_2~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_int\_1~\\
X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_int\_1~X3){\unicdbdjdcd}(X0{\unicdcdgdad}k7\_scmpds\_2~X1~X2~X3)))){\unicdcdcdhd}(\\
({\unicdcdadad} X1 .  ((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (v1\_int\_1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_int\_1~X3){\unicdbdjdcd}(X0{\unicdcdgdad}k8\_scmpds\_2~\\
X1~X2~X3)))){\unicdcdcdhd}(({\unicdcdadad} X1 .  ((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~\\
k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_int\_1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_int\_1~\\
X3){\unicdbdjdcd}(X0{\unicdcdgdad}k9\_scmpds\_2~X1~X2~X3)))){\unicdcdcdhd}(({\unicdcdadad} X1 .  ((v1\_ami\_2~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_ami\_2~\\
X2){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(v1\_int\_1~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v1\_int\_1~X4){\unicdbdjdcd}(X0{\unicdcdgdad}k11\_scmpds\_2~X1~\\
X3~X4))))){\unicdcdcdhd}(({\unicdcdadad} X1 .  ((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~\\
k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_ami\_2~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(\\
u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_int\_1~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(v1\_int\_1~X4){\unicdbdjdcd}(X0{\unicdcdgdad}k12\_scmpds\_2~X1~X2~X3~X4))))){\unicdcdcdhd}(({\unicdcdadad} X1 .  \\
((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_ami\_2~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (v1\_int\_1~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v1\_int\_1~X4){\unicdbdjdcd}(X0{\unicdcdgdad}k13\_scmpds\_2~\\
X1~X2~X3~X4))))){\unicdcdcdhd}(({\unicdcdadad} X1 .  ((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(\\
u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_ami\_2~X2){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_int\_1~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(v1\_int\_1~X4){\unicdbdjdcd}(X0{\unicdcdgdad}k14\_scmpds\_2~X1~X2~X3~X4))))){\unicdcdcdhd}(({\unicdcdadad} X1 .  \\
((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_ami\_2~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (v1\_int\_1~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v1\_int\_1~X4){\unicdbdjdcd}(X0{\unicdcdgdad}k15\_scmpds\_2~\\
X1~X2~X3~X4))))){\unicdcdcdhd}({\unicdcdadad} X1 .  ((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~\\
k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_ami\_2~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(\\
u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_int\_1~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(v1\_int\_1~X4){\unicdbdjdcd}(X0{\unicdcdgdad}k16\_scmpds\_2~X1~X2~X3~X4)))))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
