\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{t22\_integra6 (TMb92oqiA6uqHT8tj4wME4dPp6pFLehAdMp)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ k1\_numbers : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_integra5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_integra5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_comseq\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k56\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k18\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_integra5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~\\
X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}\\
(((r1\_xxreal\_0~X0~X1){\unicdcdcdhd}((r1\_xxreal\_0~X2~X3){\unicdcdcdhd}((r1\_integra5~(k3\_integra5~\\
X0~X1)~X4){\unicdcdcdhd}((v1\_comseq\_2~(k2\_partfun1~k1\_numbers~k1\_numbers~X4~\\
(k3\_integra5~X0~X1))){\unicdcdcdhd}((r1\_tarski~(k3\_integra5~X0~X1)~(k9\_xtuple\_0~\\
X4)){\unicdcdcdhd}((X2 \in k3\_integra5~X0~X1){\unicdcdcdhd}(X3 \in k3\_integra5~X0~X1))))))){\unicdbdjdcd}(\\
r1\_xxreal\_0~(k18\_complex1~(k4\_integra5~X3~X2~X4))~(k4\_integra5~\\
X2~X3~(k56\_valued\_1~k1\_numbers~k1\_numbers~X4))))))))\end{array}
\label{hyp:mgcdidpfjgogehfghgchbggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~\\
X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}\\
(((r1\_xxreal\_0~X0~X1){\unicdcdcdhd}((r1\_xxreal\_0~X2~X3){\unicdcdcdhd}((r1\_integra5~(k3\_integra5~\\
X0~X1)~X4){\unicdcdcdhd}((v1\_comseq\_2~(k2\_partfun1~k1\_numbers~k1\_numbers~X4~\\
(k3\_integra5~X0~X1))){\unicdcdcdhd}((r1\_tarski~(k3\_integra5~X0~X1)~(k9\_xtuple\_0~\\
X4)){\unicdcdcdhd}((X2 \in k3\_integra5~X0~X1){\unicdcdcdhd}(X3 \in k3\_integra5~X0~X1))))))){\unicdbdjdcd}(\\
(r1\_tarski~(k3\_integra5~X2~X3)~(k9\_xtuple\_0~(k56\_valued\_1~k1\_numbers~\\
k1\_numbers~X4))){\unicdcdcdhd}((r1\_integra5~(k3\_integra5~X2~X3)~(k56\_valued\_1~\\
k1\_numbers~k1\_numbers~X4)){\unicdcdcdhd}((v1\_comseq\_2~(k2\_partfun1~k1\_numbers~\\
k1\_numbers~(k56\_valued\_1~k1\_numbers~k1\_numbers~X4)~(k3\_integra5~\\
X2~X3))){\unicdcdcdhd}(r1\_xxreal\_0~(k18\_complex1~(k4\_integra5~X2~X3~X4))~(k4\_integra5~\\
X2~X3~(k56\_valued\_1~k1\_numbers~k1\_numbers~X4)))))))))))\end{array}
\label{hyp:mgcdfdpfjgogehfghgchbggd}
\end{equation}
\begin{theorem}\label{thm:ehcdcdpfjgogehfghgchbggd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~\\
X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}\\
(((r1\_xxreal\_0~X0~X1){\unicdcdcdhd}((r1\_xxreal\_0~X2~X3){\unicdcdcdhd}((r1\_integra5~(k3\_integra5~\\
X0~X1)~X4){\unicdcdcdhd}((v1\_comseq\_2~(k2\_partfun1~k1\_numbers~k1\_numbers~X4~\\
(k3\_integra5~X0~X1))){\unicdcdcdhd}((r1\_tarski~(k3\_integra5~X0~X1)~(k9\_xtuple\_0~\\
X4)){\unicdcdcdhd}((X2 \in k3\_integra5~X0~X1){\unicdcdcdhd}(X3 \in k3\_integra5~X0~X1))))))){\unicdbdjdcd}(\\
(r1\_tarski~(k3\_integra5~X2~X3)~(k9\_xtuple\_0~(k56\_valued\_1~k1\_numbers~\\
k1\_numbers~X4))){\unicdcdcdhd}((r1\_integra5~(k3\_integra5~X2~X3)~(k56\_valued\_1~\\
k1\_numbers~k1\_numbers~X4)){\unicdcdcdhd}((v1\_comseq\_2~(k2\_partfun1~k1\_numbers~\\
k1\_numbers~(k56\_valued\_1~k1\_numbers~k1\_numbers~X4)~(k3\_integra5~\\
X2~X3))){\unicdcdcdhd}((r1\_xxreal\_0~(k18\_complex1~(k4\_integra5~X2~X3~X4))~(\\
k4\_integra5~X2~X3~(k56\_valued\_1~k1\_numbers~k1\_numbers~X4))){\unicdcdcdhd}(\\
r1\_xxreal\_0~(k18\_complex1~(k4\_integra5~X3~X2~X4))~(k4\_integra5~\\
X2~X3~(k56\_valued\_1~k1\_numbers~k1\_numbers~X4))))))))))))\end{array}$$
\end{theorem}
\end{document}
