\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{l34\_scm\_comp (TMHiwWGcxtVE9eGRww1WKHDD67xxffeY6Za)}
\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 $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_ami\_3 : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k17\_scm\_comp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_scm\_comp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_ami\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_scm\_comp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k16\_scm\_comp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ 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 $ 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 $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~(u1\_struct\_0~k1\_scm\_comp)~(k6\_dtconstr~\\
k1\_scm\_comp)){\unicdbdjdcd}(k17\_scm\_comp~(k3\_scm\_comp~X0)=k16\_scm\_comp~\\
X0)\end{array}
\label{hyp:ehjdpfdhdgngpfdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~(u1\_struct\_0~k1\_ami\_3)){\unicdcdcdhd}\\
((v1\_funct\_1~X0){\unicdcdcdhd}((v5\_funct\_1~X0~(k2\_memstr\_0~np\_\_2~k1\_ami\_3)){\unicdcdcdhd}\\
(v1\_partfun1~X0~(u1\_struct\_0~k1\_ami\_3)))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~\\
X1~(u1\_struct\_0~k1\_scm\_comp)~(k6\_dtconstr~k1\_scm\_comp)){\unicdbdjdcd}(k12\_scm\_comp~\\
X0~(k3\_scm\_comp~X1)=k1\_funct\_1~X0~X1))\end{array}
\label{hyp:ehedpfdhdgngpfdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
r1\_xxreal\_0~X0~X0)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfihihchfgbgmgpfad}
\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}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\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}(\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}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k6\_dtconstr~k1\_scm\_comp)){\unicdbdjdcd}(m2\_subset\_1~\\
(k16\_scm\_comp~X0)~k1\_numbers~k5\_numbers)\end{array}
\label{hyp:egehpflgbdgdpfdhdgngpfdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\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}\\
((X1=k16\_scm\_comp~X0){\unicdbdjded}(k10\_ami\_3~X1=X0)))\end{array}
\label{hyp:egbdddpfdhdgngpfdgpgngah}
\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}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgcdpfihihchfgbgmgpfad}
\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:mgddedpfdhdgngpfdgpgngah}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~(u1\_struct\_0~k1\_scm\_comp)~(k6\_dtconstr~\\
k1\_scm\_comp)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~\\
(u1\_struct\_0~k1\_ami\_3)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_funct\_1~X1~(k2\_memstr\_0~\\
np\_\_2~k1\_ami\_3)){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~k1\_ami\_3)))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~(u1\_struct\_0~k1\_ami\_3)){\unicdcdcdhd}\\
((v1\_funct\_1~X2){\unicdcdcdhd}((v5\_funct\_1~X2~(k2\_memstr\_0~np\_\_2~k1\_ami\_3)){\unicdcdcdhd}\\
(v1\_partfun1~X2~(u1\_struct\_0~k1\_ami\_3)))))){\unicdbdjdcd}(({\unicdcdadad} X3 .  (m2\_subset\_1~\\
X3~k1\_numbers~k5\_numbers){\unicdbdjdcd}((r1\_xxreal\_0~X3~(k17\_scm\_comp~(k3\_scm\_comp~\\
X0))){\unicdbdjdcd}(k1\_funct\_1~X1~(k10\_ami\_3~X3)=k1\_funct\_1~X2~(k10\_ami\_3~\\
X3)))){\unicdbdjdcd}(k12\_scm\_comp~X1~(k3\_scm\_comp~X0)=k12\_scm\_comp~X2~(k3\_scm\_comp~\\
X0)))))\end{array}$$
\end{theorem}
\end{document}
