\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{t17\_scmfsa\_2 (TMFcLFb7CvkUGmaZCrf7i3KY4bbqxskzHNz)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_ami\_3 : {\iota}$ be given.
Let $ k1\_scmfsa\_2 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ k3\_scm\_inst : {\iota}$ be given.
Let $ k2\_scmfsa\_i : {\iota}$ be given.
Let $ k9\_ami\_2 : {\iota}$ be given.
Let $ k3\_ami\_2 : {\iota}$ be given.
Let $ k4\_ami\_2 : {\iota}$ be given.
Let $ k5\_scmfsa\_1 : {\iota}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ k4\_scmfsa\_1 : {\iota}$ be given.
Let $ k1\_scmfsa\_1 : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k1\_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 $ k12\_scmfsa\_1 : {\iota}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k7\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_13 : {\iota}$ be given.
Let $ k2\_scm\_inst : {\iota}$ be given.
Let $ k1\_scmfsa\_i : {\iota}$ be given.
Let $ k3\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k11\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_9 : {\iota}$ be given.
Let $ np\_\_10 : {\iota}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_11 : {\iota}$ be given.
Let $ np\_\_12 : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\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 .  (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}
{{\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}{\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}
{{({\preoh{{{v1\_xboole\_0}~{k3\_scm\_inst}}}})}{\unicdcdcdhd}{({{v5\_compos\_0}~{k3\_scm\_inst}})}}\label{hyp:ggdghdpfdhdgngpfjgogdheh}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k2\_scmfsa\_i}}}})}{\unicdcdcdhd}{({{v5\_compos\_0}~{k2\_scmfsa\_i}})}}\label{hyp:ggdggdpfdhdgngggdhbgpfjg}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k3\_scm\_inst}}}})}{\unicdcdcdhd}{({{v3\_compos\_0}~{k3\_scm\_inst}})}}\label{hyp:ggdggdpfdhdgngpfjgogdheh}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k2\_scmfsa\_i}}}})}{\unicdcdcdhd}{({{v3\_compos\_0}~{k2\_scmfsa\_i}})}}\label{hyp:ggdgfdpfdhdgngggdhbgpfjg}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k3\_scm\_inst}}}})}{\unicdcdcdhd}{({{v2\_compos\_0}~{k3\_scm\_inst}})}}\label{hyp:ggdgfdpfdhdgngpfjgogdheh}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k2\_scmfsa\_i}}}})}{\unicdcdcdhd}{({{v2\_compos\_0}~{k2\_scmfsa\_i}})}}\label{hyp:ggdgedpfdhdgngggdhbgpfjg}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k3\_scm\_inst}}}})}{\unicdcdcdhd}{({{v1\_compos\_0}~{k3\_scm\_inst}})}}\label{hyp:ggdgedpfdhdgngpfjgogdheh}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k2\_scmfsa\_i}}}})}{\unicdcdcdhd}{({{v1\_compos\_0}~{k2\_scmfsa\_i}})}}\label{hyp:ggdgddpfdhdgngggdhbgpfjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k9\_ami\_2){\unicdcdcdhd}((v1\_funct\_2~k9\_ami\_2~k3\_scm\_inst~(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~k9\_ami\_2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k3\_scm\_inst~(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:egehpflgjdpfbgngjgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_relat\_1~k5\_scmfsa\_1){\unicdcdcdhd}((v4\_relat\_1~k5\_scmfsa\_1~np\_\_3){\unicdcdcdhd}(\\
(v1\_funct\_1~k5\_scmfsa\_1){\unicdcdcdhd}(v1\_partfun1~k5\_scmfsa\_1~np\_\_3)))\end{array}
\label{hyp:egehpflgfdpfdhdgngggdhbgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k4\_scmfsa\_1){\unicdcdcdhd}((v1\_funct\_2~k4\_scmfsa\_1~k1\_scmfsa\_1~\\
np\_\_3){\unicdcdcdhd}(m1\_subset\_1~k4\_scmfsa\_1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_scmfsa\_1~\\
np\_\_3))))\end{array}
\label{hyp:egehpflgedpfdhdgngggdhbgpfbd}
\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}
{{({{{v1\_extpro\_1}~{k1\_scmfsa\_2}}~{np\_\_3}})}{\unicdcdcdhd}{({{{l1\_extpro\_1}~{k1\_scmfsa\_2}}~{np\_\_3}})}}\label{hyp:egehpflgbdpfdhdgngggdhbgpfcd}
\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}
{{({{{v1\_extpro\_1}~{k1\_ami\_3}}~{np\_\_2}})}{\unicdcdcdhd}{({{{l1\_extpro\_1}~{k1\_ami\_3}}~{np\_\_2}})}}\label{hyp:egehpflgbdpfbgngjgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k12\_scmfsa\_1){\unicdcdcdhd}((v1\_funct\_2~k12\_scmfsa\_1~k2\_scmfsa\_i~\\
(k1\_funct\_2~(k4\_card\_3~(k3\_relat\_1~k4\_scmfsa\_1~k5\_scmfsa\_1))~\\
(k4\_card\_3~(k3\_relat\_1~k4\_scmfsa\_1~k5\_scmfsa\_1)))){\unicdcdcdhd}(m1\_subset\_1~\\
k12\_scmfsa\_1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k2\_scmfsa\_i~(k1\_funct\_2~\\
(k4\_card\_3~(k3\_relat\_1~k4\_scmfsa\_1~k5\_scmfsa\_1))~(k4\_card\_3~\\
(k3\_relat\_1~k4\_scmfsa\_1~k5\_scmfsa\_1)))))))\end{array}
\label{hyp:egehpflgbdcdpfdhdgngggdhbgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k2\_xboole\_0~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}((X3 \in X0){\unicdcdcdid}(X3 \in X1)))\end{array}
\label{hyp:egddpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k2\_scmfsa\_i=k2\_xboole\_0~(k2\_xboole\_0~k3\_scm\_inst~(ReplSep4~\\
(toset~({\uniddcgcg} X0 : \iota .  m2\_subset\_1~X0~k4\_ordinal1~(k7\_card\_1~np\_\_13)))~\\
({\uniddcgcg} X0 : \iota .  toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~X1~k2\_scm\_inst))~\\
({\uniddcgcg} X0 : \iota .  {\uniddcgcg} X1 : \iota .  toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~X2~k2\_scm\_inst))~\\
({\uniddcgcg} X0 : \iota .  {\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  toset~({\uniddcgcg} X3 : \iota .  m1\_subset\_1~\\
X3~k1\_scmfsa\_i))~({\uniddcgcg} X0 : \iota .  {\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \\
\iota .  X0 \in k2\_tarski~np\_\_9~np\_\_10)~({\uniddcgcg} X0 : \iota .  {\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \\
\iota .  {\uniddcgcg} X3 : \iota .  k3\_xtuple\_0~X0~k1\_xboole\_0~(k11\_finseq\_1~X1~X3~\\
X2))))~(ReplSep3~(toset~({\uniddcgcg} X0 : \iota .  m2\_subset\_1~X0~k4\_ordinal1~\\
(k7\_card\_1~np\_\_13)))~({\uniddcgcg} X0 : \iota .  toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~\\
X1~k2\_scm\_inst))~({\uniddcgcg} X0 : \iota .  {\uniddcgcg} X1 : \iota .  toset~({\uniddcgcg} X2 : \iota .  \\
m1\_subset\_1~X2~k1\_scmfsa\_i))~({\uniddcgcg} X0 : \iota .  {\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \\
\iota .  X0 \in k2\_tarski~np\_\_11~np\_\_12)~({\uniddcgcg} X0 : \iota .  {\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \\
\iota .  k3\_xtuple\_0~X0~k1\_xboole\_0~(k10\_finseq\_1~X1~X2)))\end{array}
\label{hyp:egcdpfdhdgngggdhbgpfjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k1\_scmfsa\_2=g1\_extpro\_1~np\_\_3~k1\_scmfsa\_1~(k1\_funct\_7~k5\_numbers~\\
k1\_scmfsa\_1)~k2\_scmfsa\_i~k4\_scmfsa\_1~k5\_scmfsa\_1~k12\_scmfsa\_1\end{array}
\label{hyp:egbdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k1\_ami\_3=g1\_extpro\_1~np\_\_2~k1\_ami\_2~(k1\_funct\_7~k5\_numbers~k1\_ami\_2)~\\
k3\_scm\_inst~k3\_ami\_2~k4\_ami\_2~k9\_ami\_2\end{array}
\label{hyp:egbdpfbgngjgpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_xboole\_0}~{X0}}~{X1}}={{{k2\_xboole\_0}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfihcgpgpgmgfgpfad}
\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:ehbdhdpfdhdgngggdhbgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_ami\_3)){\unicdbdjdcd}(m1\_subset\_1~\\
X0~(u1\_compos\_1~k1\_scmfsa\_2))\end{array}$$
\end{theorem}
\end{document}
