\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{t7\_scm\_comp (TMbKETm85Fu9KSntxck7hHbbWSe4wnxxnPZ)}
\maketitle
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_scm\_comp : {\iota}$ be given.
Let $ k6\_dtconstr : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k15\_scm\_comp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_scm\_comp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_ami\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_ami\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_scm\_comp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\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 $ k4\_ordinal1 : {\iota}$ be given.
Let $ k3\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_dtconstr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_lang1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_dtconstr : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k5\_trees\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_dtconstr : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_lang1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_dtconstr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_dtconstr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_bintree1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k14\_scm\_comp : {\iota}$ be given.
Let $ k9\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_ami\_3 : {\iota}$ be given.
Let $ k16\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k7\_dtconstr : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_bintree1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_pre\_poly : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_scm\_comp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_ordinal4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k15\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k13\_scm\_comp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
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}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k5\_afinsq\_1}~{X0}}={{k3\_afinsq\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))))){\unicdcdcdhd}(m1\_subset\_1~X3~X0))){\unicdbdjdcd}(k3\_funct\_2~X0~\\
X1~X2~X3=k1\_funct\_1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_dtconstr~X0){\unicdcdcdhd}(l1\_lang1~X0))){\unicdbdjdcd}\\
((\preoh v1\_xboole\_0~(k6\_dtconstr~X0)){\unicdcdcdhd}(m1\_subset\_1~(k6\_dtconstr~\\
X0)~(k1\_zfmisc\_1~(u1\_struct\_0~X0))))\end{array}
\label{hyp:egehpflggdpfegehdgpgogdhehch}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k5\_numbers}}~{({{k1\_zfmisc\_1}~{k1\_numbers}})}}\label{hyp:egehpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k6\_dtconstr~k1\_scm\_comp)){\unicdbdjdcd}(m1\_dtconstr~\\
(k3\_scm\_comp~X0)~(u1\_struct\_0~k1\_scm\_comp)~(k5\_trees\_3~(u1\_struct\_0~\\
k1\_scm\_comp))~(k4\_dtconstr~k1\_scm\_comp))\end{array}
\label{hyp:egehpflgddpfdhdgngpfdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v2\_struct\_0~k1\_scm\_comp){\unicdcdcdhd}((v1\_lang1~k1\_scm\_comp){\unicdcdcdhd}((v1\_dtconstr~\\
k1\_scm\_comp){\unicdcdcdhd}((v2\_dtconstr~k1\_scm\_comp){\unicdcdcdhd}((v3\_dtconstr~k1\_scm\_comp){\unicdcdcdhd}\\
((v3\_bintree1~k1\_scm\_comp){\unicdcdcdhd}(l1\_lang1~k1\_scm\_comp))))))\end{array}
\label{hyp:egehpflgbdpfdhdgngpfdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k14\_scm\_comp){\unicdcdcdhd}((v1\_funct\_2~k14\_scm\_comp~(k4\_dtconstr~\\
k1\_scm\_comp)~(k9\_funct\_2~k5\_numbers~(k8\_afinsq\_1~(u1\_compos\_1~\\
k1\_ami\_3)))){\unicdcdcdhd}(m1\_subset\_1~k14\_scm\_comp~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k4\_dtconstr~k1\_scm\_comp)~(k9\_funct\_2~k5\_numbers~(k8\_afinsq\_1~\\
(u1\_compos\_1~k1\_ami\_3)))))))\end{array}
\label{hyp:egehpflgbdedpfdhdgngpfdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k3\_afinsq\_1}~{X0}}={{{k16\_funcop\_1}~{k6\_numbers}}~{X0}}}}\label{hyp:egbdpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_dtconstr~X0~(u1\_struct\_0~k1\_scm\_comp)~(k5\_trees\_3~\\
(u1\_struct\_0~k1\_scm\_comp))~(k4\_dtconstr~k1\_scm\_comp)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}(k15\_scm\_comp~X0~X1=k1\_funct\_1~\\
(k3\_funct\_2~(k4\_dtconstr~k1\_scm\_comp)~(k9\_funct\_2~k5\_numbers~\\
(k8\_afinsq\_1~(u1\_compos\_1~k1\_ami\_3)))~k14\_scm\_comp~X0)~X1))\end{array}
\label{hyp:egbdcdpfdhdgngpfdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~(k4\_dtconstr~k1\_scm\_comp)~\\
(k9\_funct\_2~k5\_numbers~(k8\_afinsq\_1~(u1\_compos\_1~k1\_ami\_3)))){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_dtconstr~k1\_scm\_comp)~\\
(k9\_funct\_2~k5\_numbers~(k8\_afinsq\_1~(u1\_compos\_1~k1\_ami\_3)))))))){\unicdbdjdcd}\\
((X0=k14\_scm\_comp){\unicdbdjded}(({\unicdcdadad} X1 .  (m2\_subset\_1~X1~(u1\_struct\_0~\\
k1\_scm\_comp)~(k6\_dtconstr~k1\_scm\_comp)){\unicdbdjdcd}({\unicdcdaddd} X2 .  ((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_2~X2~k5\_numbers~(k8\_afinsq\_1~(u1\_compos\_1~k1\_ami\_3))){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k8\_afinsq\_1~\\
(u1\_compos\_1~k1\_ami\_3))))))){\unicdcdcdhd}((X2=k3\_funct\_2~(k4\_dtconstr~\\
k1\_scm\_comp)~(k9\_funct\_2~k5\_numbers~(k8\_afinsq\_1~(u1\_compos\_1~\\
k1\_ami\_3)))~X0~(k3\_scm\_comp~X1)){\unicdcdcdhd}({\unicdcdadad} X3 .  (m2\_subset\_1~X3~\\
k1\_numbers~k5\_numbers){\unicdbdjdcd}(k3\_funct\_2~k5\_numbers~(k8\_afinsq\_1~\\
(u1\_compos\_1~k1\_ami\_3))~X2~X3=k5\_afinsq\_1~(k2\_ami\_3~(k10\_ami\_3~\\
X3)~(k4\_scm\_comp~X1))))))){\unicdcdcdhd}({\unicdcdadad} X1 .  (m2\_subset\_1~X1~(u1\_struct\_0~\\
k1\_scm\_comp)~(k7\_dtconstr~k1\_scm\_comp)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_dtconstr~\\
X2~(u1\_struct\_0~k1\_scm\_comp)~(k5\_trees\_3~(u1\_struct\_0~k1\_scm\_comp))~\\
(k4\_dtconstr~k1\_scm\_comp)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_dtconstr~X3~(u1\_struct\_0~\\
k1\_scm\_comp)~(k5\_trees\_3~(u1\_struct\_0~k1\_scm\_comp))~(k4\_dtconstr~\\
k1\_scm\_comp)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~k1\_scm\_comp)){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~k1\_scm\_comp)){\unicdbdjdcd}(\preoh (X4=\\
k1\_bintree1~(u1\_struct\_0~k1\_scm\_comp)~X2){\unicdcdcdhd}((X5=k1\_bintree1~\\
(u1\_struct\_0~k1\_scm\_comp)~X3){\unicdcdcdhd}((r1\_lang1~k1\_scm\_comp~X1~(k4\_pre\_poly~\\
(u1\_struct\_0~k1\_scm\_comp)~X4~X5)){\unicdcdcdhd}({\unicdcdadad} X6 .  ((v1\_funct\_1~X6){\unicdcdcdhd}\\
((v1\_funct\_2~X6~k5\_numbers~(k8\_afinsq\_1~(u1\_compos\_1~k1\_ami\_3))){\unicdcdcdhd}\\
(m1\_subset\_1~X6~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k8\_afinsq\_1~\\
(u1\_compos\_1~k1\_ami\_3))))))){\unicdbdjdcd}({\unicdcdadad} X7 .  ((v1\_funct\_1~X7){\unicdcdcdhd}\\
((v1\_funct\_2~X7~k5\_numbers~(k8\_afinsq\_1~(u1\_compos\_1~k1\_ami\_3))){\unicdcdcdhd}\\
(m1\_subset\_1~X7~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k8\_afinsq\_1~\\
(u1\_compos\_1~k1\_ami\_3))))))){\unicdbdjdcd}({\unicdcdadad} X8 .  ((v1\_funct\_1~X8){\unicdcdcdhd}\\
((v1\_funct\_2~X8~k5\_numbers~(k8\_afinsq\_1~(u1\_compos\_1~k1\_ami\_3))){\unicdcdcdhd}\\
(m1\_subset\_1~X8~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k8\_afinsq\_1~\\
(u1\_compos\_1~k1\_ami\_3))))))){\unicdbdjdcd}(\preoh (X6=k3\_funct\_2~(k4\_dtconstr~\\
k1\_scm\_comp)~(k9\_funct\_2~k5\_numbers~(k8\_afinsq\_1~(u1\_compos\_1~\\
k1\_ami\_3)))~X0~(k2\_scm\_comp~X1~X2~X3)){\unicdcdcdhd}((X7=k3\_funct\_2~(k4\_dtconstr~\\
k1\_scm\_comp)~(k9\_funct\_2~k5\_numbers~(k8\_afinsq\_1~(u1\_compos\_1~\\
k1\_ami\_3)))~X0~X2){\unicdcdcdhd}((X8=k3\_funct\_2~(k4\_dtconstr~k1\_scm\_comp)~\\
(k9\_funct\_2~k5\_numbers~(k8\_afinsq\_1~(u1\_compos\_1~k1\_ami\_3)))~\\
X0~X3){\unicdcdcdhd}({\unicdcdadad} X9 .  (m2\_subset\_1~X9~k1\_numbers~k5\_numbers){\unicdbdjdcd}(k3\_funct\_2~\\
k5\_numbers~(k8\_afinsq\_1~(u1\_compos\_1~k1\_ami\_3))~X6~X9=k1\_ordinal4~\\
(k15\_afinsq\_1~(u1\_compos\_1~k1\_ami\_3)~(k3\_funct\_2~k5\_numbers~\\
(k8\_afinsq\_1~(u1\_compos\_1~k1\_ami\_3))~X7~X9)~(k3\_funct\_2~k5\_numbers~\\
(k8\_afinsq\_1~(u1\_compos\_1~k1\_ami\_3))~X8~(k2\_nat\_1~X9~np\_\_1)))~\\
(k13\_scm\_comp~X1~X9)))))))))))))))))))\end{array}
\label{hyp:egbdbdpfdhdgngpfdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_xboole\_0~X1))\end{array}
\label{hyp:dgdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehhdpfdhdgngpfdgpgngah}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~(u1\_struct\_0~k1\_scm\_comp)~(k6\_dtconstr~\\
k1\_scm\_comp)){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}\\
(k15\_scm\_comp~(k3\_scm\_comp~X0)~X1=k5\_afinsq\_1~(k2\_ami\_3~(k10\_ami\_3~\\
X1)~(k4\_scm\_comp~X0))))\end{array}$$
\end{theorem}
\end{document}
