\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{t2\_scm\_comp (TMLHYErix3KpdC6qjQdn8rFig9UpstniQ9T)}
\maketitle
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_scm\_comp : {\iota}$ be given.
Let $ k7\_dtconstr : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ np\_\_4 : {\iota}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ np\_\_0 : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_5 : {\iota}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_dtconstr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_lang1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_lang1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_dtconstr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_dtconstr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_bintree1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (k4\_tarski~X0~X1 \in \\
k2\_zfmisc\_1~X2~X3){\unicdbdjded}((X0 \in X2){\unicdcdcdhd}(X1 \in X3))\end{array}
\label{hyp:ehidhdpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\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}((v2\_xxreal\_0~np\_\_4){\unicdcdcdhd}(m2\_subset\_1~np\_\_4~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_4~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_4~k1\_numbers))\end{array}
\label{hyp:dhahdgedpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_3){\unicdcdcdhd}(m2\_subset\_1~np\_\_3~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_3~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_3~k1\_numbers))\end{array}
\label{hyp:dhahdgddpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_2){\unicdcdcdhd}(m2\_subset\_1~np\_\_2~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_2~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_2~k1\_numbers))\end{array}
\label{hyp:dhahdgcdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{np\_\_0}}\label{hyp:dhahdgadpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_5}}~{np\_\_4}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchfdpfched}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_5}}~{np\_\_3}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchfdpfchdd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_5}}~{np\_\_2}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchfdpfchcd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_5}}~{np\_\_1}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchfdpfchbd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_5}}~{np\_\_0}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchfdpfchad}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_1}}~{np\_\_0}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdpfchad}
\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}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{{k7\_dtconstr}~{k1\_scm\_comp}}={{{k2\_zfmisc\_1}~{np\_\_1}}~{np\_\_5}}}\label{hyp:mgedpfdhdgngpfdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}np\_\_5=ReplSep~(toset~({\uniddcgcg} X0 : \iota .  m2\_subset\_1~X0~k1\_numbers~k5\_numbers))~\\
({\uniddcgcg} X0 : \iota .  \preoh r1\_xxreal\_0~np\_\_5~X0)~({\uniddcgcg} X0 : \iota .  X0)\end{array}
\label{hyp:mgcdpfdhdgngpfdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}np\_\_1=ReplSep~(toset~({\uniddcgcg} X0 : \iota .  m2\_subset\_1~X0~k1\_numbers~k5\_numbers))~\\
({\uniddcgcg} X0 : \iota .  \preoh r1\_xxreal\_0~np\_\_1~X0)~({\uniddcgcg} X0 : \iota .  X0)\end{array}
\label{hyp:mgbdpfdhdgngpfdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_dtconstr~X0){\unicdcdcdhd}(l1\_lang1~X0))){\unicdbdjdcd}\\
((\preoh v1\_xboole\_0~(k7\_dtconstr~X0)){\unicdcdcdhd}(m1\_subset\_1~(k7\_dtconstr~\\
X0)~(k1\_zfmisc\_1~(u1\_struct\_0~X0))))\end{array}
\label{hyp:egehpflghdpfegehdgpgogdhehch}
\end{equation}
Assume the following.
\begin{equation}
{{{{m2\_subset\_1}~{k6\_numbers}}~{k1\_numbers}}~{k5\_numbers}}\label{hyp:egehpflggdpfogfhngcgfgchdh}
\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 .  (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:ehcdpfdhdgngpfdgpgngah}
$$\begin{array}{c}(m2\_subset\_1~(k4\_tarski~k6\_numbers~k6\_numbers)~(u1\_struct\_0~\\
k1\_scm\_comp)~(k7\_dtconstr~k1\_scm\_comp)){\unicdcdcdhd}((m2\_subset\_1~(k4\_tarski~\\
k6\_numbers~np\_\_1)~(u1\_struct\_0~k1\_scm\_comp)~(k7\_dtconstr~k1\_scm\_comp)){\unicdcdcdhd}\\
((m2\_subset\_1~(k4\_tarski~k6\_numbers~np\_\_2)~(u1\_struct\_0~k1\_scm\_comp)~\\
(k7\_dtconstr~k1\_scm\_comp)){\unicdcdcdhd}((m2\_subset\_1~(k4\_tarski~k6\_numbers~\\
np\_\_3)~(u1\_struct\_0~k1\_scm\_comp)~(k7\_dtconstr~k1\_scm\_comp)){\unicdcdcdhd}\\
(m2\_subset\_1~(k4\_tarski~k6\_numbers~np\_\_4)~(u1\_struct\_0~k1\_scm\_comp)~\\
(k7\_dtconstr~k1\_scm\_comp)))))\end{array}$$
\end{theorem}
\end{document}
