\documentclass{article}
\newtheorem{axiom}{Axiom}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t56\_integr19 (TMY9Vcf1xHSX42FNfDau7AeT6CqYcBDYuQD)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ 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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_real\_ns1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_integr18 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_integra5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_integr19 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_nfcont\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_integr18 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ r1\_ndiff\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_ndiff\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_partfun1 : {{\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 .  ((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}(m2\_subset\_1~\\
X3~k1\_numbers~k5\_numbers)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~(u1\_struct\_0~(k4\_real\_ns1~\\
X3)))))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~X5){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k1\_numbers~(u1\_struct\_0~(k4\_real\_ns1~X3)))))){\unicdbdjdcd}\\
(((r1\_xxreal\_0~X0~X1){\unicdcdcdhd}((r1\_integr18~(k4\_real\_ns1~X3)~(k3\_integra5~\\
X0~X1)~X5){\unicdcdcdhd}((v1\_integr19~(k2\_partfun1~k1\_numbers~(u1\_struct\_0~\\
(k4\_real\_ns1~X3))~X5~(k3\_integra5~X0~X1))~(k4\_real\_ns1~X3)~k1\_numbers){\unicdcdcdhd}\\
((r1\_tarski~(k3\_integra5~X0~X1)~(k1\_relset\_1~k1\_numbers~X5)){\unicdcdcdhd}\\
((r1\_tarski~(k2\_rcomp\_1~X0~X1)~(k1\_relset\_1~k1\_numbers~X4)){\unicdcdcdhd}(\\
({\unicdcdadad} X6 .  (v1\_xreal\_0~X6){\unicdbdjdcd}((X6 \in k2\_rcomp\_1~X0~X1){\unicdbdjdcd}(k1\_funct\_1~\\
X4~X6=k6\_integr18~(k4\_real\_ns1~X3)~X5~X0~X6))){\unicdcdcdhd}((X2 \in k2\_rcomp\_1~\\
X0~X1){\unicdcdcdhd}(r1\_nfcont\_3~(k4\_real\_ns1~X3)~X5~X2)))))))){\unicdbdjdcd}((r1\_ndiff\_3~\\
(k4\_real\_ns1~X3)~X4~X2){\unicdcdcdhd}(k1\_ndiff\_3~(k4\_real\_ns1~X3)~X4~X2=k7\_partfun1~\\
(u1\_struct\_0~(k4\_real\_ns1~X3))~X5~X2))))))))\end{array}
\label{hyp:ehfdfdpfjgogehfghgchbdjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~\\
X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~(u1\_struct\_0~\\
(k4\_real\_ns1~X0)))))){\unicdbdjdcd}({\unicdcdaddd} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~(u1\_struct\_0~(k4\_real\_ns1~\\
X0)))))){\unicdcdcdhd}((r1\_tarski~(k2\_rcomp\_1~X1~X2)~(k1\_relset\_1~k1\_numbers~\\
X4)){\unicdcdcdhd}({\unicdcdadad} X5 .  (v1\_xreal\_0~X5){\unicdbdjdcd}((X5 \in k2\_rcomp\_1~X1~X2){\unicdbdjdcd}(k1\_funct\_1~\\
X4~X5=k6\_integr18~(k4\_real\_ns1~X0)~X3~X1~X5))))))))\end{array}
\label{hyp:mghdedpfjgogehfghgchbdjd}
\end{equation}
\begin{theorem}\label{thm:ehfdgdpfjgogehfghgchbdjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}(m2\_subset\_1~\\
X3~k1\_numbers~k5\_numbers)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~(u1\_struct\_0~(k4\_real\_ns1~\\
X3)))))){\unicdbdjdcd}(\preoh (r1\_xxreal\_0~X0~X1){\unicdcdcdhd}((r1\_integr18~(k4\_real\_ns1~X3)~\\
(k3\_integra5~X0~X1)~X4){\unicdcdcdhd}((v1\_integr19~(k2\_partfun1~k1\_numbers~\\
(u1\_struct\_0~(k4\_real\_ns1~X3))~X4~(k3\_integra5~X0~X1))~(k4\_real\_ns1~\\
X3)~k1\_numbers){\unicdcdcdhd}((r1\_tarski~(k3\_integra5~X0~X1)~(k1\_relset\_1~\\
k1\_numbers~X4)){\unicdcdcdhd}((X2 \in k2\_rcomp\_1~X0~X1){\unicdcdcdhd}((r1\_nfcont\_3~(k4\_real\_ns1~\\
X3)~X4~X2){\unicdcdcdhd}({\unicdcdadad} X5 .  ((v1\_funct\_1~X5){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k1\_numbers~(u1\_struct\_0~(k4\_real\_ns1~X3)))))){\unicdbdjdcd}\\
(\preoh (r1\_tarski~(k2\_rcomp\_1~X0~X1)~(k1\_relset\_1~k1\_numbers~X5)){\unicdcdcdhd}\\
(({\unicdcdadad} X6 .  (v1\_xreal\_0~X6){\unicdbdjdcd}((X6 \in k2\_rcomp\_1~X0~X1){\unicdbdjdcd}(k1\_funct\_1~\\
X5~X6=k6\_integr18~(k4\_real\_ns1~X3)~X4~X0~X6))){\unicdcdcdhd}((r1\_ndiff\_3~(k4\_real\_ns1~\\
X3)~X5~X2){\unicdcdcdhd}(k1\_ndiff\_3~(k4\_real\_ns1~X3)~X5~X2=k7\_partfun1~(u1\_struct\_0~\\
(k4\_real\_ns1~X3))~X4~X2)))))))))))))))\end{array}$$
\end{theorem}
\end{document}
