\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{t27\_scmpds\_2 (TMMMAYcFM4t4QDV8LzNoBFjssAowLmA5rZC)}
\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 $ k2\_compos\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\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 $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k9\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k2\_ami\_2 : {\iota}$ be given.
Let $ k2\_scm\_inst : {\iota}$ be given.
Let $ k12\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_numbers : {\iota}$ be given.
Let $ np\_\_14 : {\iota}$ be given.
Let $ k1\_ami\_2 : {\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 $ np\_\_2 : {\iota}$ be given.
Let $ np\_\_3 : {\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 $ 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 $ k7\_finseq\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\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 $ v1\_compos\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_compos\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_compos\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_compos\_0 : {{\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 $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ g1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}}$ be given.
Let $ k1\_scmpds\_i : {\iota}$ be given.
Let $ k6\_scmpds\_1 : {\iota}$ be given.
Let $ k3\_ami\_2 : {\iota}$ be given.
Let $ k4\_ami\_2 : {\iota}$ be given.
Let $ v1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ u2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u2\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{np\_\_1}}}}\label{hyp:dhahdgbdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k9\_finseq\_1}~{X0}}={{k5\_finseq\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{k2\_ami\_2}={k2\_scm\_inst}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfbgngjgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~X0)){\unicdbdjdcd}\\
(k12\_finseq\_1~X0~X1=k5\_finseq\_1~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdcdpfggjgogdhfgbhpfbd}
\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}((X0 \in \\
k1\_tarski~(k3\_xtuple\_0~k6\_numbers~k1\_xboole\_0~k1\_xboole\_0)){\unicdbdjdcd}\\
(k2\_compos\_0~(u1\_compos\_1~k1\_scmpds\_2)~X0=k6\_numbers))\end{array}
\label{hyp:mgedjdpfdhdgngahegdhpfcd}
\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 .  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 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  ((m1\_subset\_1~X2~X1){\unicdcdcdhd}(((v1\_compos\_0~X3){\unicdcdcdhd}((v2\_compos\_0~\\
X3){\unicdcdcdhd}((v3\_compos\_0~X3){\unicdcdcdhd}(v5\_compos\_0~X3)))){\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))))){\unicdcdcdhd}(((v1\_relat\_1~X5){\unicdcdcdhd}((v4\_relat\_1~X5~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X5){\unicdcdcdhd}(v1\_partfun1~X5~X0)))){\unicdcdcdhd}((v1\_funct\_1~X6){\unicdcdcdhd}((v1\_funct\_2~X6~\\
X3~(k1\_funct\_2~(k4\_card\_3~(k3\_relat\_1~X4~X5))~(k4\_card\_3~(k3\_relat\_1~\\
X4~X5)))){\unicdcdcdhd}(m1\_subset\_1~X6~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X3~(k1\_funct\_2~\\
(k4\_card\_3~(k3\_relat\_1~X4~X5))~(k4\_card\_3~(k3\_relat\_1~X4~X5)))))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X7 .  {\unicdcdadad} X8 .  {\unicdcdadad} X9 .  {\unicdcdadad} X10 .  {\unicdcdadad} X11 .  {\unicdcdadad} X12 .  \\
{\unicdcdadad} X13 .  (g1\_extpro\_1~X0~X1~X2~X3~X4~X5~X6=g1\_extpro\_1~X7~X8~X9~\\
X10~X11~X12~X13){\unicdbdjdcd}((X0=X7){\unicdcdcdhd}((X1=X8){\unicdcdcdhd}((X2=X9){\unicdcdcdhd}((X3=X10){\unicdcdcdhd}((X4=\\
X11){\unicdcdcdhd}((X5=X12){\unicdcdcdhd}(X6=X13))))))))\end{array}
\label{hyp:ggchfgfgpfhgbdpffgihehahchpgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v5\_compos\_0}~{k1\_scmpds\_i}}\label{hyp:ggdggdpfdhdgngahegdhpfjg}
\end{equation}
Assume the following.
\begin{equation}
{{v3\_compos\_0}~{k1\_scmpds\_i}}\label{hyp:ggdgfdpfdhdgngahegdhpfjg}
\end{equation}
Assume the following.
\begin{equation}
{{v2\_compos\_0}~{k1\_scmpds\_i}}\label{hyp:ggdgedpfdhdgngahegdhpfjg}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_compos\_0}~{k1\_scmpds\_i}}\label{hyp:ggdgddpfdhdgngahegdhpfjg}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k2\_scm\_inst}}}}\label{hyp:ggdgbdpfdhdgngpfjgogdheh}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_ami\_2}}}}\label{hyp:ggdgbdpfbgngjgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k6\_scmpds\_1){\unicdcdcdhd}((v1\_funct\_2~k6\_scmpds\_1~k1\_scmpds\_i~\\
(k1\_funct\_2~(k4\_card\_3~(k3\_relat\_1~k3\_ami\_2~k4\_ami\_2))~(k4\_card\_3~\\
(k3\_relat\_1~k3\_ami\_2~k4\_ami\_2)))){\unicdcdcdhd}(m1\_subset\_1~k6\_scmpds\_1~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_scmpds\_i~(k1\_funct\_2~(k4\_card\_3~\\
(k3\_relat\_1~k3\_ami\_2~k4\_ami\_2))~(k4\_card\_3~(k3\_relat\_1~k3\_ami\_2~\\
k4\_ami\_2)))))))\end{array}
\label{hyp:egehpflggdpfdhdgngahegdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_relat\_1~k4\_ami\_2){\unicdcdcdhd}((v4\_relat\_1~k4\_ami\_2~np\_\_2){\unicdcdcdhd}((v1\_funct\_1~\\
k4\_ami\_2){\unicdcdcdhd}(v1\_partfun1~k4\_ami\_2~np\_\_2)))\end{array}
\label{hyp:egehpflgedpfbgngjgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k3\_ami\_2){\unicdcdcdhd}((v1\_funct\_2~k3\_ami\_2~k1\_ami\_2~np\_\_2){\unicdcdcdhd}\\
(m1\_subset\_1~k3\_ami\_2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_ami\_2~np\_\_2))))\end{array}
\label{hyp:egehpflgddpfbgngjgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k2\_ami\_2}}~{({{k1\_zfmisc\_1}~{k1\_ami\_2}})}}\label{hyp:egehpflgcdpfbgngjgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{({{{v1\_extpro\_1}~{k1\_scmpds\_2}}~{np\_\_2}})}{\unicdcdcdhd}{({{{l1\_extpro\_1}~{k1\_scmpds\_2}}~{np\_\_2}})}}\label{hyp:egehpflgbdpfdhdgngahegdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{m1\_subset\_1}~{({{{k1\_funct\_7}~{X0}}~{X1}})}}~{X1}}}}\label{hyp:egehpflgbdpfggfhogdgehpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}\\
(k4\_scmpds\_2~X0=k3\_xtuple\_0~np\_\_1~k1\_xboole\_0~(k9\_finseq\_1~X0))\end{array}
\label{hyp:egfdpfdhdgngahegdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k1\_scmpds\_2=g1\_extpro\_1~np\_\_2~k1\_ami\_2~(k1\_funct\_7~k5\_numbers~\\
k1\_ami\_2)~k1\_scmpds\_i~k3\_ami\_2~k4\_ami\_2~k6\_scmpds\_1\end{array}
\label{hyp:egbdpfdhdgngahegdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_ami\_2}~{X0}})}{\unicdbdjded}{({{X0} \in {k2\_ami\_2}})}}}\label{hyp:egbdgdpfbgngjgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (l1\_extpro\_1~X1~X0){\unicdbdjdcd}((v1\_extpro\_1~X1~X0){\unicdbdjdcd}\\
(X1=g1\_extpro\_1~X0~(u1\_struct\_0~X1)~(u2\_struct\_0~X1)~(u1\_compos\_1~\\
X1)~(u1\_memstr\_0~X0~X1)~(u2\_memstr\_0~X0~X1)~(u1\_extpro\_1~X0~X1)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpffgihehahchpgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdhdpfdhdgngahegdhpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdbdjdcd}(\preoh (k2\_compos\_0~\\
(u1\_compos\_1~k1\_scmpds\_2)~X0=np\_\_1){\unicdcdcdhd}({\unicdcdadad} X1 .  ((v1\_ami\_2~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}(X0{\unicdcdgdad}k4\_scmpds\_2~\\
X1)))\end{array}$$
\end{theorem}
\end{document}
