\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{t19\_sublemma (TMQCbEoUFraTpAjyDNiovB71z4HtQMu7ymu)}
\maketitle
Let $ m1\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_valuat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k16\_substut1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k38\_substut1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k3\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_valuat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_valuat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ k39\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_sublemma : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ k1\_sublemma : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_sublemma : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k5\_sublemma : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k37\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k20\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k13\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k9\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_cqc\_lang : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_cqc\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k16\_substut1~\\
X0)){\unicdbdjdcd}(k37\_substut1~X0~(k20\_substut1~X0~X1)=k13\_qc\_lang1~X0~(k37\_substut1~\\
X0~X1)))\end{array}
\label{hyp:ehcdjdpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m2\_funct\_2~X2~(k3\_qc\_lang1~X0)~X1~(k2\_valuat\_1~X0~X1)){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(k16\_substut1~X0)~(k38\_substut1~X0)){\unicdbdjdcd}\\
(r2\_relset\_1~(k3\_qc\_lang1~X0)~X1~(k3\_sublemma~X0~X3~X1~X2)~(k3\_sublemma~\\
X0~(k5\_sublemma~X0~X3)~X1~X2)))))\end{array}
\label{hyp:ehbdidpfdhfhcgmgfgngngbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m2\_funct\_2~X2~(k3\_qc\_lang1~X0)~X1~(k2\_valuat\_1~X0~X1)){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(k9\_qc\_lang1~X0)~(k3\_cqc\_lang~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_valuat\_1~X4~X0~X1){\unicdbdjdcd}((r1\_valuat\_1~X0~X1~(k6\_cqc\_lang~\\
X0~X3)~X4~X2){\unicdbdjded}(\preoh r1\_valuat\_1~X0~X1~X3~X4~X2))))))\end{array}
\label{hyp:ehbdhdpfghbgmgfhbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m1\_valuat\_1~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_funct\_2~X3~(\\
k3\_qc\_lang1~X0)~X1~(k2\_valuat\_1~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_subset\_1~\\
X4~(k16\_substut1~X0)~(k38\_substut1~X0)){\unicdbdjdcd}((\preoh r1\_sublemma~X0~X4~X1~\\
(k1\_sublemma~X0~X1~X3~(k3\_sublemma~X0~X4~X1~X3))~X2){\unicdbdjded}(r1\_sublemma~\\
X0~(k5\_sublemma~X0~X4)~X1~(k1\_sublemma~X0~X1~X3~(k3\_sublemma~X0~X4~\\
X1~X3))~X2))))))\end{array}
\label{hyp:ehbdhdpfdhfhcgmgfgngngbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}((r2\_relset\_1~X0~X1~X2~X3){\unicdbdjded}(X2=X3))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfchfgmgdhfgehpfbd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_funct\_2~\\
X2~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_funct\_2~X3~X0~X1~X2){\unicdbdjded}(m1\_subset\_1~X3~\\
X2))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k3\_cqc\_lang~\\
X0))){\unicdbdjdcd}(k6\_cqc\_lang~X0~X1=k13\_qc\_lang1~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfdgbhdgpfmgbgoghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k38\_substut1~\\
X0))){\unicdbdjdcd}(k5\_sublemma~X0~X1=k20\_substut1~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfdhfhcgmgfgngngbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k38\_substut1~\\
X0))){\unicdbdjdcd}(k39\_substut1~X0~X1=k37\_substut1~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddjdpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{m1\_qc\_lang1}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{({{k38\_substut1}~{X0}})}}}})}}}\label{hyp:ggdghdpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{m1\_qc\_lang1}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{({{k3\_cqc\_lang}~{X0}})}}}})}}}\label{hyp:ggdgcdpfdgbhdgpfmgbgoghg}
\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){\unicdbdjdcd}(m1\_subset\_1~X2~X0))\end{array}
\label{hyp:egehpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k38\_substut1~\\
X0))){\unicdbdjdcd}(m2\_subset\_1~(k5\_sublemma~X0~X1)~(k16\_substut1~X0)~(k38\_substut1~\\
X0))\end{array}
\label{hyp:egehpflgfdpfdhfhcgmgfgngngbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}\\
((m1\_subset\_1~X1~(k38\_substut1~X0)){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k2\_valuat\_1~X0~X2))))){\unicdbdjdcd}((v1\_funct\_1~(k3\_sublemma~X0~X1~X2~X3)){\unicdcdcdhd}\\
(m1\_subset\_1~(k3\_sublemma~X0~X1~X2~X3)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k3\_qc\_lang1~X0)~X2))))\end{array}
\label{hyp:egehpflgddpfdhfhcgmgfgngngbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}(m1\_subset\_1~(k3\_cqc\_lang~X0)~(k1\_zfmisc\_1~\\
(k9\_qc\_lang1~X0)))\end{array}
\label{hyp:egehpflgddpfdgbhdgpfmgbgoghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k38\_substut1~\\
X0))){\unicdbdjdcd}(m2\_subset\_1~(k39\_substut1~X0~X1)~(k9\_qc\_lang1~X0)~(k3\_cqc\_lang~\\
X0))\end{array}
\label{hyp:egehpflgddjdpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}(m1\_subset\_1~(k38\_substut1~X0)~(\\
k1\_zfmisc\_1~(k16\_substut1~X0)))\end{array}
\label{hyp:egehpflgddidpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}(\preoh v1\_xboole\_0~X1)){\unicdbdjdcd}\\
(m1\_funct\_2~(k2\_valuat\_1~X0~X1)~(k3\_qc\_lang1~X0)~X1)\end{array}
\label{hyp:egehpflgcdpfghbgmgfhbgehpfbd}
\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:ehbdjdpfdhfhcgmgfgngngbg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m1\_valuat\_1~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_subset\_1~X3~\\
(k16\_substut1~X0)~(k38\_substut1~X0)){\unicdbdjdcd}(({\unicdcdadad} X4 .  (m2\_funct\_2~\\
X4~(k3\_qc\_lang1~X0)~X1~(k2\_valuat\_1~X0~X1)){\unicdbdjdcd}((r1\_valuat\_1~X0~X1~\\
(k39\_substut1~X0~X3)~X2~X4){\unicdbdjded}(r1\_sublemma~X0~X3~X1~(k1\_sublemma~X0~\\
X1~X4~(k3\_sublemma~X0~X3~X1~X4))~X2))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_funct\_2~X4~\\
(k3\_qc\_lang1~X0)~X1~(k2\_valuat\_1~X0~X1)){\unicdbdjdcd}((r1\_valuat\_1~X0~X1~(k39\_substut1~\\
X0~(k5\_sublemma~X0~X3))~X2~X4){\unicdbdjded}(r1\_sublemma~X0~(k5\_sublemma~X0~X3)~\\
X1~(k1\_sublemma~X0~X1~X4~(k3\_sublemma~X0~(k5\_sublemma~X0~X3)~X1~X4))~\\
X2)))))))\end{array}$$
\end{theorem}
\end{document}
