\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{t56\_sublemma (TMWuqddmmYqKjTsB5yYWpfzt5RzWEbX8bF1)}
\maketitle
Let $ m1\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k2\_valuat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k16\_substut1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k38\_substut1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k7\_sublemma : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v3\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ 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 $ k12\_sublemma : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k35\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k32\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_sublemma : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k14\_sublemma : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k13\_sublemma : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ m1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_valuat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_sublemma : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_funct\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_cqc\_lang : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_cqc\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k15\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_substut1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_sublemma : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k2\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~X1~(k2\_qc\_lang1~\\
X0)~(k3\_qc\_lang1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m2\_funct\_2~X3~(k3\_qc\_lang1~X0)~X2~(k2\_valuat\_1~X0~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m2\_subset\_1~X4~(k16\_substut1~X0)~(k38\_substut1~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(m1\_substut1~X5~X0~(k7\_sublemma~X0~X4~X1)){\unicdbdjdcd}((v3\_substut1~(k7\_sublemma~\\
X0~X4~X1)~X0){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~X2){\unicdbdjdcd}(r2\_relset\_1~(k3\_qc\_lang1~\\
X0)~X2~(k13\_sublemma~X0~X4~X1~X5~X2~(k1\_sublemma~X0~X2~X3~(k12\_sublemma~\\
X0~X2~(k35\_substut1~X0~(k32\_substut1~X0~(k9\_sublemma~X0~(k7\_sublemma~\\
X0~X4~X1)~X5)))~X6)))~(k13\_sublemma~X0~X4~X1~X5~X2~X3)))))))))\end{array}
\label{hyp:ehfdfdpfdhfhcgmgfgngngbg}
\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 .  {\unicdcdadad} X2 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~(k38\_substut1~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k3\_qc\_lang1~X0)))){\unicdbdjdcd}(k7\_sublemma~\\
X0~X1~X2=k4\_tarski~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfdhfhcgmgfgngngbg}
\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}\\
(k2\_valuat\_1~X0~X1=k1\_valuat\_1~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfghbgmgfhbgehpfbd}
\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}(k2\_sublemma~X0~X1=k1\_xtuple\_0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfdhfhcgmgfgngngbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}\\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((m1\_subset\_1~X2~(k2\_valuat\_1~X0~X1)){\unicdcdcdhd}((v1\_funct\_1~\\
X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_qc\_lang1~X0)~\\
X1))))))){\unicdbdjdcd}(k1\_sublemma~X0~X1~X2~X3=k1\_funct\_4~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfdhfhcgmgfgngngbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~(k3\_qc\_lang1~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k3\_cqc\_lang~X0)))){\unicdbdjdcd}(k11\_cqc\_lang~\\
X0~X1~X2=k15\_qc\_lang1~X0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdbdpfdgbhdgpfmgbgoghg}
\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\_qc\_lang1}~{X0}})}}}})}}}\label{hyp:ggdgddpfbhdgpfmgbgoghgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{m1\_qc\_lang1}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{({{k2\_qc\_lang1}~{X0}})}}}})}}}\label{hyp:ggdgcdpfbhdgpfmgbgoghgbd}
\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 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_funct\_2~\\
X2~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_funct\_2~X3~X0~X1~X2){\unicdbdjdcd}((v1\_funct\_1~X3){\unicdcdcdhd}\\
((v1\_funct\_2~X3~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1))))))\end{array}
\label{hyp:egehpfngcdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k2\_zfmisc\_1~\\
(k16\_substut1~X0)~(k3\_qc\_lang1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_substut1~\\
X2~X0~X1){\unicdbdjdcd}(m1\_subset\_1~X2~(k1\_substut1~X0)))\end{array}
\label{hyp:egehpfngbdpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}(((v1\_sublemma~\\
X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k2\_zfmisc\_1~(k16\_substut1~X0)~(k3\_qc\_lang1~\\
X0)))){\unicdcdcdhd}(m1\_substut1~X2~X0~X1))){\unicdbdjdcd}(m2\_subset\_1~(k9\_sublemma~X0~\\
X1~X2)~(k16\_substut1~X0)~(k38\_substut1~X0))\end{array}
\label{hyp:egehpflgjdpfdhfhcgmgfgngngbg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{m1\_qc\_lang1}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{({{k9\_qc\_lang1}~{X0}})}}}})}}}\label{hyp:egehpflgjdpfbhdgpfmgbgoghgbd}
\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~(k3\_qc\_lang1~X0)){\unicdcdcdhd}((m1\_subset\_1~X2~(k9\_qc\_lang1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_substut1~X0))))){\unicdbdjdcd}((v1\_finset\_1~(k7\_substut1~\\
X0~X1~X2~X3)){\unicdcdcdhd}(m1\_subset\_1~(k7\_substut1~X0~X1~X2~X3)~(k1\_substut1~\\
X0)))\end{array}
\label{hyp:egehpflghdpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~(k38\_substut1~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k3\_qc\_lang1~X0)))){\unicdbdjdcd}((\\
v1\_sublemma~(k7\_sublemma~X0~X1~X2)~X0){\unicdcdcdhd}(m1\_subset\_1~(k7\_sublemma~\\
X0~X1~X2)~(k2\_zfmisc\_1~(k16\_substut1~X0)~(k3\_qc\_lang1~X0))))\end{array}
\label{hyp:egehpflghdpfdhfhcgmgfgngngbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X2~X3)))){\unicdbdjdcd}(m1\_subset\_1~(k4\_relset\_1~\\
X0~X1~X2~X3~X4~X5)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X3)))\end{array}
\label{hyp:egehpflgedpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}(m1\_subset\_1~(k3\_qc\_lang1~X0)~(k1\_zfmisc\_1~\\
(k2\_qc\_lang1~X0)))\end{array}
\label{hyp:egehpflgddpfbhdgpfmgbgoghgbd}
\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 .  (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}(m1\_subset\_1~X1~(k2\_zfmisc\_1~\\
(k9\_qc\_lang1~X0)~(k1\_substut1~X0)))){\unicdbdjdcd}(m2\_subset\_1~(k35\_substut1~\\
X0~X1)~(k2\_qc\_lang1~X0)~(k3\_qc\_lang1~X0))\end{array}
\label{hyp:egehpflgddfdpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k16\_substut1~\\
X0))){\unicdbdjdcd}(m1\_subset\_1~(k32\_substut1~X0~X1)~(k2\_zfmisc\_1~(k9\_qc\_lang1~\\
X0)~(k1\_substut1~X0)))\end{array}
\label{hyp:egehpflgddcdpfdhfhcgdhehfhehbd}
\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 .  {\unicdcdadad} X1 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_substut1~\\
X0))){\unicdbdjdcd}((v1\_funct\_1~(k2\_substut1~X0~X1)){\unicdcdcdhd}(m1\_subset\_1~(k2\_substut1~\\
X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_qc\_lang1~X0)~(k3\_qc\_lang1~\\
X0)))))\end{array}
\label{hyp:egehpflgcdpfdhfhcgdhehfhehbd}
\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~(k2\_sublemma~X0~X1)~(k9\_qc\_lang1~X0)~(k3\_cqc\_lang~\\
X0))\end{array}
\label{hyp:egehpflgcdpfdhfhcgmgfgngngbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}\\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((m1\_subset\_1~X2~(k2\_valuat\_1~X0~X1)){\unicdcdcdhd}((v1\_funct\_1~\\
X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_qc\_lang1~X0)~\\
X1))))))){\unicdbdjdcd}(m2\_funct\_2~(k1\_sublemma~X0~X1~X2~X3)~(k3\_qc\_lang1~X0)~\\
X1~(k2\_valuat\_1~X0~X1))\end{array}
\label{hyp:egehpflgbdpfdhfhcgmgfgngngbg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{m1\_qc\_lang1}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{({{k16\_substut1}~{X0}})}}}})}}}\label{hyp:egehpflgbdgdpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~(k3\_qc\_lang1~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k9\_qc\_lang1~X0)))){\unicdbdjdcd}(m1\_subset\_1~\\
(k15\_qc\_lang1~X0~X1~X2)~(k9\_qc\_lang1~X0))\end{array}
\label{hyp:egehpflgbdfdpfbhdgpfmgbgoghgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((m1\_qc\_lang1~X0){\unicdcdcdhd}((m1\_subset\_1~X1~(k38\_substut1~X0)){\unicdcdcdhd}((m1\_subset\_1~\\
X2~(k3\_qc\_lang1~X0)){\unicdcdcdhd}((m1\_substut1~X3~X0~(k7\_sublemma~X0~X1~X2)){\unicdcdcdhd}\\
((\preoh v1\_xboole\_0~X4){\unicdcdcdhd}(m1\_subset\_1~X5~(k2\_valuat\_1~X0~X4))))))){\unicdbdjdcd}\\
((v1\_funct\_1~(k13\_sublemma~X0~X1~X2~X3~X4~X5)){\unicdcdcdhd}(m1\_subset\_1~(k13\_sublemma~\\
X0~X1~X2~X3~X4~X5)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_qc\_lang1~X0)~X4))))\end{array}
\label{hyp:egehpflgbdddpfdhfhcgmgfgngngbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}\\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((m1\_subset\_1~X2~(k3\_qc\_lang1~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X3~X1)))){\unicdbdjdcd}((v1\_funct\_1~(k12\_sublemma~X0~X1~X2~X3)){\unicdcdcdhd}(m1\_subset\_1~\\
(k12\_sublemma~X0~X1~X2~X3)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_qc\_lang1~\\
X0)~X1))))\end{array}
\label{hyp:egehpflgbdcdpfdhfhcgmgfgngngbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~X1~(k16\_substut1~\\
X0)~(k38\_substut1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~(k2\_qc\_lang1~\\
X0)~(k3\_qc\_lang1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_substut1~X3~X0~(k7\_sublemma~\\
X0~X1~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  (\preoh v1\_xboole\_0~X4){\unicdbdjdcd}({\unicdcdadad} X5 .  (m2\_funct\_2~\\
X5~(k3\_qc\_lang1~X0)~X4~(k2\_valuat\_1~X0~X4)){\unicdbdjdcd}(k13\_sublemma~X0~X1~\\
X2~X3~X4~X5=k4\_relset\_1~(k3\_qc\_lang1~X0)~(k3\_qc\_lang1~X0)~(k3\_qc\_lang1~\\
X0)~X4~(k2\_substut1~X0~(k7\_substut1~X0~X2~(k11\_cqc\_lang~X0~X2~(k2\_sublemma~\\
X0~X1))~X3))~X5))))))\end{array}
\label{hyp:egidpfdhfhcgmgfgngngbg}
\end{equation}
\begin{theorem}\label{thm:ehfdgdpfdhfhcgmgfgngngbg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~X1~(k2\_qc\_lang1~\\
X0)~(k3\_qc\_lang1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_valuat\_1~X3~X0~X2){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_funct\_2~X4~(k3\_qc\_lang1~\\
X0)~X2~(k2\_valuat\_1~X0~X2)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m2\_subset\_1~X5~(k16\_substut1~\\
X0)~(k38\_substut1~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_substut1~X6~X0~(k7\_sublemma~\\
X0~X5~X1)){\unicdbdjdcd}((v3\_substut1~(k7\_sublemma~X0~X5~X1)~X0){\unicdbdjdcd}(({\unicdcdadad} X7 .  \\
(m1\_subset\_1~X7~X2){\unicdbdjdcd}(r1\_sublemma~X0~X5~X2~(k1\_sublemma~X0~X2~(k1\_sublemma~\\
X0~X2~X4~(k12\_sublemma~X0~X2~(k35\_substut1~X0~(k32\_substut1~X0~(k9\_sublemma~\\
X0~(k7\_sublemma~X0~X5~X1)~X6)))~X7))~(k14\_sublemma~X0~X2~(k13\_sublemma~\\
X0~X5~X1~X6~X2~(k1\_sublemma~X0~X2~X4~(k12\_sublemma~X0~X2~(k35\_substut1~\\
X0~(k32\_substut1~X0~(k9\_sublemma~X0~(k7\_sublemma~X0~X5~X1)~X6)))~\\
X7)))~(k12\_sublemma~X0~X2~X1~X7)))~X3)){\unicdbdjded}({\unicdcdadad} X7 .  (m1\_subset\_1~\\
X7~X2){\unicdbdjdcd}(r1\_sublemma~X0~X5~X2~(k1\_sublemma~X0~X2~(k1\_sublemma~X0~X2~\\
X4~(k12\_sublemma~X0~X2~(k35\_substut1~X0~(k32\_substut1~X0~(k9\_sublemma~\\
X0~(k7\_sublemma~X0~X5~X1)~X6)))~X7))~(k14\_sublemma~X0~X2~(k13\_sublemma~\\
X0~X5~X1~X6~X2~X4)~(k12\_sublemma~X0~X2~X1~X7)))~X3))))))))))\end{array}$$
\end{theorem}
\end{document}
