\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{t32\_substut1 (TMZhFRY4U5p6Fj1VthnZh1fGeqvi98vrhPQ)}
\maketitle
Let $ m1\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k16\_substut1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v7\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k37\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k36\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k31\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\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 $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v2\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_cqc\_lang : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v4\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k16\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k18\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k26\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k19\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v5\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k13\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k27\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v6\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k14\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k28\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k29\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
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~(k37\_substut1~X0~X1)~(k9\_qc\_lang1~X0))\end{array}
\label{hyp:egehpflgddhdpfdhfhcgdhehfhehbd}
\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~(k16\_substut1~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k9\_qc\_lang1~X0)))){\unicdbdjdcd}(m1\_subset\_1~\\
(k36\_substut1~X0~X1~X2)~(k9\_qc\_lang1~X0))\end{array}
\label{hyp:egehpflgddgdpfdhfhcgdhehfhehbd}
\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~(k31\_substut1~X0~X1)~(k16\_substut1~X0))\end{array}
\label{hyp:egehpflgddbdpfdhfhcgdhehfhehbd}
\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}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k9\_qc\_lang1~X0)){\unicdbdjdcd}((X2=k37\_substut1~\\
X0~X1){\unicdbdjded}({\unicdcdaddd} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k16\_substut1~\\
X0)~(k9\_qc\_lang1~X0)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k16\_substut1~X0)~(k9\_qc\_lang1~X0)))))){\unicdcdcdhd}((X2=k3\_funct\_2~(k16\_substut1~\\
X0)~(k9\_qc\_lang1~X0)~X3~X1){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k16\_substut1~\\
X0)){\unicdbdjdcd}(((v2\_substut1~X4~X0){\unicdbdjdcd}(k3\_funct\_2~(k16\_substut1~X0)~(k9\_qc\_lang1~\\
X0)~X3~X4=k5\_cqc\_lang~X0)){\unicdcdcdhd}(((v4\_substut1~X4~X0){\unicdbdjdcd}(k3\_funct\_2~\\
(k16\_substut1~X0)~(k9\_qc\_lang1~X0)~X3~X4=k10\_qc\_lang1~X0~(k16\_qc\_lang1~\\
X0~(k18\_substut1~X0~X4))~(k3\_substut1~X0~(k26\_substut1~X0~X4)~(k19\_substut1~\\
X0~X4)))){\unicdcdcdhd}(((v5\_substut1~X4~X0){\unicdbdjdcd}(k3\_funct\_2~(k16\_substut1~X0)~\\
(k9\_qc\_lang1~X0)~X3~X4=k13\_qc\_lang1~X0~(k3\_funct\_2~(k16\_substut1~\\
X0)~(k9\_qc\_lang1~X0)~X3~(k27\_substut1~X0~X4)))){\unicdcdcdhd}(((v6\_substut1~\\
X4~X0){\unicdbdjdcd}(k3\_funct\_2~(k16\_substut1~X0)~(k9\_qc\_lang1~X0)~X3~X4=k14\_qc\_lang1~\\
X0~(k3\_funct\_2~(k16\_substut1~X0)~(k9\_qc\_lang1~X0)~X3~(k28\_substut1~\\
X0~X4))~(k3\_funct\_2~(k16\_substut1~X0)~(k9\_qc\_lang1~X0)~X3~(k29\_substut1~\\
X0~X4)))){\unicdcdcdhd}((v7\_substut1~X4~X0){\unicdbdjdcd}(k3\_funct\_2~(k16\_substut1~X0)~\\
(k9\_qc\_lang1~X0)~X3~X4=k36\_substut1~X0~X4~(k3\_funct\_2~(k16\_substut1~\\
X0)~(k9\_qc\_lang1~X0)~X3~(k31\_substut1~X0~X4))))))))))))))\end{array}
\label{hyp:egddidpfdhfhcgdhehfhehbd}
\end{equation}
\begin{theorem}\label{thm:ehddcdpfdhfhcgdhehfhehbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k16\_substut1~\\
X0)){\unicdbdjdcd}((v7\_substut1~X1~X0){\unicdbdjdcd}(k37\_substut1~X0~X1=k36\_substut1~X0~\\
X1~(k37\_substut1~X0~(k31\_substut1~X0~X1)))))\end{array}$$
\end{theorem}
\end{document}
