\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\_sublemma (TMZxttpDkdu7N2uRagk39oXFXUobB171TKS)}
\maketitle
Let $ m1\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k6\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_card\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_substut1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k26\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k17\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k16\_substut1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
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~X2)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchcdpfchfgmgdhfgehpfbd}
\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}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k5\_numbers){\unicdcdcdhd}(m1\_qc\_lang1~\\
X1)){\unicdbdjdcd}(\preoh v1\_xboole\_0~(k8\_qc\_lang1~X1~X0))\end{array}
\label{hyp:ggdghdpfbhdgpfmgbgoghgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{m1\_qc\_lang1}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{({{k6\_qc\_lang1}~{X0}})}}}})}}}\label{hyp:ggdggdpfbhdgpfmgbgoghgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((m1\_qc\_lang1~\\
X0){\unicdcdcdhd}((m1\_subset\_1~X1~k5\_numbers){\unicdcdcdhd}((m1\_subset\_1~X2~(k8\_qc\_lang1~\\
X0~X1)){\unicdcdcdhd}(((v3\_card\_1~X3~X1){\unicdcdcdhd}(m1\_finseq\_1~X3~(k2\_qc\_lang1~X0))){\unicdcdcdhd}\\
(m1\_subset\_1~X4~(k1\_substut1~X0)))))){\unicdbdjdcd}(v4\_substut1~(k17\_substut1~\\
X0~X2~X3~X4)~X0)\end{array}
\label{hyp:ggdgfdpfdhfhcgdhehfhehbd}
\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 .  (m2\_finseq\_1~X1~X0){\unicdbdjdcd}((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_finseq\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
X0)))))\end{array}
\label{hyp:egehpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~k5\_numbers)){\unicdbdjdcd}\\
(m1\_subset\_1~(k8\_qc\_lang1~X0~X1)~(k1\_zfmisc\_1~(k6\_qc\_lang1~X0)))\end{array}
\label{hyp:egehpflgidpfbhdgpfmgbgoghgbd}
\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~(k6\_qc\_lang1~X0)){\unicdcdcdhd}((m1\_finseq\_1~X2~(k2\_qc\_lang1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_substut1~X0))))){\unicdbdjdcd}(m1\_subset\_1~(k17\_substut1~\\
X0~X1~X2~X3)~(k16\_substut1~X0))\end{array}
\label{hyp:egehpflgbdhdpfdhfhcgdhehfhehbd}
\end{equation}
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}((v4\_substut1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~(k2\_qc\_lang1~\\
X0)){\unicdbdjdcd}((X2=k26\_substut1~X0~X1){\unicdbdjded}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~k5\_numbers){\unicdcdcdhd}\\
({\unicdcdaddd} X4 .  (m2\_subset\_1~X4~(k6\_qc\_lang1~X0)~(k8\_qc\_lang1~X0~X3)){\unicdcdcdhd}\\
({\unicdcdaddd} X5 .  ((v3\_card\_1~X5~X3){\unicdcdcdhd}(m2\_finseq\_1~X5~(k2\_qc\_lang1~X0))){\unicdcdcdhd}\\
({\unicdcdaddd} X6 .  (m1\_subset\_1~X6~(k1\_substut1~X0)){\unicdcdcdhd}((r2\_relset\_1~\\
k5\_numbers~(k2\_qc\_lang1~X0)~X2~X5){\unicdcdcdhd}(X1=k17\_substut1~X0~X4~X5~X6))))))))))\end{array}
\label{hyp:egcdjdpfdhfhcgdhehfhehbd}
\end{equation}
\begin{theorem}\label{thm:ehhdpfdhfhcgmgfgngngbg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k5\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m2\_subset\_1~X2~(k6\_qc\_lang1~X0)~(k8\_qc\_lang1~X0~X1)){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(k6\_qc\_lang1~X0)~(k8\_qc\_lang1~X0~X1)){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  ((v5\_relat\_1~X4~(k3\_qc\_lang1~X0)){\unicdcdcdhd}((v3\_card\_1~X4~\\
X1){\unicdcdcdhd}(m2\_finseq\_1~X4~(k2\_qc\_lang1~X0)))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v5\_relat\_1~\\
X5~(k3\_qc\_lang1~X0)){\unicdcdcdhd}((v3\_card\_1~X5~X1){\unicdcdcdhd}(m2\_finseq\_1~X5~(k2\_qc\_lang1~\\
X0)))){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(k1\_substut1~X0)){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m1\_subset\_1~X7~(k1\_substut1~X0)){\unicdbdjdcd}((r2\_relset\_1~k5\_numbers~(\\
k2\_qc\_lang1~X0)~(k26\_substut1~X0~(k17\_substut1~X0~X2~X4~X6))~(k26\_substut1~\\
X0~(k17\_substut1~X0~X3~X5~X7))){\unicdbdjdcd}(r2\_relset\_1~k5\_numbers~(k2\_qc\_lang1~\\
X0)~X4~X5)))))))))\end{array}$$
\end{theorem}
\end{document}
