\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{l70\_substut1 (TMLno1Ura5di5RHUiSRGaB5M42VKnvGKyFm)}
\maketitle
Let $ m1\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ k16\_substut1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\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 $ v2\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ 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.
Let $ v7\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ 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 $ r2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}\iota{\unicdbdjdcd}\iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X1 : \iota{\unicdbdjdcd}\iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X2 : \\
\iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X3 : \iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  {\unicdcdadad} X6 .  \\
{\unicdcdadad} X7 .  {\unicdcdadad} X8 .  ((m1\_qc\_lang1~X8){\unicdcdcdhd}((\preoh v1\_xboole\_0~X7){\unicdcdcdhd}\\
(((v1\_funct\_1~X6){\unicdcdcdhd}((v1\_funct\_2~X6~(k16\_substut1~X8)~X7){\unicdcdcdhd}(m1\_subset\_1~\\
X6~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k16\_substut1~X8)~X7))))){\unicdcdcdhd}(((v1\_funct\_1~\\
X5){\unicdcdcdhd}((v1\_funct\_2~X5~(k16\_substut1~X8)~X7){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k16\_substut1~X8)~X7))))){\unicdcdcdhd}((m1\_subset\_1~X4~X7){\unicdcdcdhd}\\
(({\unicdcdadad} X9 .  m1\_subset\_1~(X3~X9)~X7){\unicdcdcdhd}(({\unicdcdadad} X9 .  m1\_subset\_1~\\
(X2~X9)~X7){\unicdcdcdhd}(({\unicdcdadad} X9 .  {\unicdcdadad} X10 .  m1\_subset\_1~(X1~X9~X10)~X7){\unicdcdcdhd}\\
({\unicdcdadad} X9 .  {\unicdcdadad} X10 .  {\unicdcdadad} X11 .  m1\_subset\_1~(X0~X9~X10~X11)~\\
X7))))))))){\unicdbdjdcd}((({\unicdcdadad} X9 .  (m1\_subset\_1~X9~(k16\_substut1~X8)){\unicdbdjdcd}\\
({\unicdcdadad} X10 .  (m1\_subset\_1~X10~X7){\unicdbdjdcd}({\unicdcdadad} X11 .  (m1\_subset\_1~\\
X11~X7){\unicdbdjdcd}(((v2\_substut1~X9~X8){\unicdbdjdcd}(k3\_funct\_2~(k16\_substut1~X8)~X7~\\
X6~X9=X4)){\unicdcdcdhd}(((v4\_substut1~X9~X8){\unicdbdjdcd}(k3\_funct\_2~(k16\_substut1~X8)~\\
X7~X6~X9=X3~X9)){\unicdcdcdhd}((((v5\_substut1~X9~X8){\unicdcdcdhd}(X10=k3\_funct\_2~(k16\_substut1~\\
X8)~X7~X6~(k27\_substut1~X8~X9))){\unicdbdjdcd}(k3\_funct\_2~(k16\_substut1~X8)~\\
X7~X6~X9=X2~X10)){\unicdcdcdhd}((((v6\_substut1~X9~X8){\unicdcdcdhd}((X10=k3\_funct\_2~(k16\_substut1~\\
X8)~X7~X6~(k28\_substut1~X8~X9)){\unicdcdcdhd}(X11=k3\_funct\_2~(k16\_substut1~\\
X8)~X7~X6~(k29\_substut1~X8~X9)))){\unicdbdjdcd}(k3\_funct\_2~(k16\_substut1~X8)~\\
X7~X6~X9=X1~X10~X11)){\unicdcdcdhd}(((v7\_substut1~X9~X8){\unicdcdcdhd}(X10=k3\_funct\_2~(k16\_substut1~\\
X8)~X7~X6~(k31\_substut1~X8~X9))){\unicdbdjdcd}(k3\_funct\_2~(k16\_substut1~X8)~\\
X7~X6~X9=X0~X8~X9~X10))))))))){\unicdcdcdhd}({\unicdcdadad} X9 .  (m1\_subset\_1~X9~(k16\_substut1~\\
X8)){\unicdbdjdcd}({\unicdcdadad} X10 .  (m1\_subset\_1~X10~X7){\unicdbdjdcd}({\unicdcdadad} X11 .  (m1\_subset\_1~\\
X11~X7){\unicdbdjdcd}(((v2\_substut1~X9~X8){\unicdbdjdcd}(k3\_funct\_2~(k16\_substut1~X8)~X7~\\
X5~X9=X4)){\unicdcdcdhd}(((v4\_substut1~X9~X8){\unicdbdjdcd}(k3\_funct\_2~(k16\_substut1~X8)~\\
X7~X5~X9=X3~X9)){\unicdcdcdhd}((((v5\_substut1~X9~X8){\unicdcdcdhd}(X10=k3\_funct\_2~(k16\_substut1~\\
X8)~X7~X5~(k27\_substut1~X8~X9))){\unicdbdjdcd}(k3\_funct\_2~(k16\_substut1~X8)~\\
X7~X5~X9=X2~X10)){\unicdcdcdhd}((((v6\_substut1~X9~X8){\unicdcdcdhd}((X10=k3\_funct\_2~(k16\_substut1~\\
X8)~X7~X5~(k28\_substut1~X8~X9)){\unicdcdcdhd}(X11=k3\_funct\_2~(k16\_substut1~\\
X8)~X7~X5~(k29\_substut1~X8~X9)))){\unicdbdjdcd}(k3\_funct\_2~(k16\_substut1~X8)~\\
X7~X5~X9=X1~X10~X11)){\unicdcdcdhd}(((v7\_substut1~X9~X8){\unicdcdcdhd}(X10=k3\_funct\_2~(k16\_substut1~\\
X8)~X7~X5~(k31\_substut1~X8~X9))){\unicdbdjdcd}(k3\_funct\_2~(k16\_substut1~X8)~\\
X7~X5~X9=X0~X8~X9~X10)))))))))){\unicdbdjdcd}(r2\_funct\_2~(k16\_substut1~X8)~X7~\\
X6~X5))\end{array}
\label{hyp:dhedpfdhfhcgdhehfhehbd}
\end{equation}
\begin{theorem}\label{thm:mghdadpfdhfhcgdhehfhehbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((\\
v1\_funct\_2~X1~(k16\_substut1~X0)~(k9\_qc\_lang1~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k16\_substut1~X0)~(k9\_qc\_lang1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k16\_substut1~X0)~\\
(k9\_qc\_lang1~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k16\_substut1~X0)~(k9\_qc\_lang1~X0)))))){\unicdbdjdcd}((({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(k16\_substut1~X0)){\unicdbdjdcd}(((v2\_substut1~X3~X0){\unicdbdjdcd}(k3\_funct\_2~(k16\_substut1~\\
X0)~(k9\_qc\_lang1~X0)~X1~X3=k5\_cqc\_lang~X0)){\unicdcdcdhd}(((v4\_substut1~X3~\\
X0){\unicdbdjdcd}(k3\_funct\_2~(k16\_substut1~X0)~(k9\_qc\_lang1~X0)~X1~X3=k10\_qc\_lang1~\\
X0~(k16\_qc\_lang1~X0~(k18\_substut1~X0~X3))~(k3\_substut1~X0~(k26\_substut1~\\
X0~X3)~(k19\_substut1~X0~X3)))){\unicdcdcdhd}(((v5\_substut1~X3~X0){\unicdbdjdcd}(k3\_funct\_2~\\
(k16\_substut1~X0)~(k9\_qc\_lang1~X0)~X1~X3=k13\_qc\_lang1~X0~(k3\_funct\_2~\\
(k16\_substut1~X0)~(k9\_qc\_lang1~X0)~X1~(k27\_substut1~X0~X3)))){\unicdcdcdhd}\\
(((v6\_substut1~X3~X0){\unicdbdjdcd}(k3\_funct\_2~(k16\_substut1~X0)~(k9\_qc\_lang1~\\
X0)~X1~X3=k14\_qc\_lang1~X0~(k3\_funct\_2~(k16\_substut1~X0)~(k9\_qc\_lang1~\\
X0)~X1~(k28\_substut1~X0~X3))~(k3\_funct\_2~(k16\_substut1~X0)~(k9\_qc\_lang1~\\
X0)~X1~(k29\_substut1~X0~X3)))){\unicdcdcdhd}((v7\_substut1~X3~X0){\unicdbdjdcd}(k3\_funct\_2~\\
(k16\_substut1~X0)~(k9\_qc\_lang1~X0)~X1~X3=k36\_substut1~X0~X3~(k3\_funct\_2~\\
(k16\_substut1~X0)~(k9\_qc\_lang1~X0)~X1~(k31\_substut1~X0~X3))))))))){\unicdcdcdhd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k16\_substut1~X0)){\unicdbdjdcd}(((v2\_substut1~\\
X3~X0){\unicdbdjdcd}(k3\_funct\_2~(k16\_substut1~X0)~(k9\_qc\_lang1~X0)~X2~X3=k5\_cqc\_lang~\\
X0)){\unicdcdcdhd}(((v4\_substut1~X3~X0){\unicdbdjdcd}(k3\_funct\_2~(k16\_substut1~X0)~(k9\_qc\_lang1~\\
X0)~X2~X3=k10\_qc\_lang1~X0~(k16\_qc\_lang1~X0~(k18\_substut1~X0~X3))~\\
(k3\_substut1~X0~(k26\_substut1~X0~X3)~(k19\_substut1~X0~X3)))){\unicdcdcdhd}(\\
((v5\_substut1~X3~X0){\unicdbdjdcd}(k3\_funct\_2~(k16\_substut1~X0)~(k9\_qc\_lang1~\\
X0)~X2~X3=k13\_qc\_lang1~X0~(k3\_funct\_2~(k16\_substut1~X0)~(k9\_qc\_lang1~\\
X0)~X2~(k27\_substut1~X0~X3)))){\unicdcdcdhd}(((v6\_substut1~X3~X0){\unicdbdjdcd}(k3\_funct\_2~\\
(k16\_substut1~X0)~(k9\_qc\_lang1~X0)~X2~X3=k14\_qc\_lang1~X0~(k3\_funct\_2~\\
(k16\_substut1~X0)~(k9\_qc\_lang1~X0)~X2~(k28\_substut1~X0~X3))~(k3\_funct\_2~\\
(k16\_substut1~X0)~(k9\_qc\_lang1~X0)~X2~(k29\_substut1~X0~X3)))){\unicdcdcdhd}\\
((v7\_substut1~X3~X0){\unicdbdjdcd}(k3\_funct\_2~(k16\_substut1~X0)~(k9\_qc\_lang1~\\
X0)~X2~X3=k36\_substut1~X0~X3~(k3\_funct\_2~(k16\_substut1~X0)~(k9\_qc\_lang1~\\
X0)~X2~(k31\_substut1~X0~X3)))))))))){\unicdbdjdcd}(r2\_funct\_2~(k16\_substut1~\\
X0)~(k9\_qc\_lang1~X0)~X1~X2))))\end{array}$$
\end{theorem}
\end{document}
