\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{t39\_integr14 (TMSqEuNBVbU29QruaHjiTmW1oP4AWyEVUDY)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_measure5 : {{\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 $ k1\_numbers : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k16\_sin\_cos : {\iota}$ be given.
Let $ k19\_sin\_cos : {\iota}$ be given.
Let $ k5\_square\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k2\_fdiff\_9 : {\iota}$ be given.
Let $ v1\_fcont\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_integra5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_seq\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_seq\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r2\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_integra5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_comseq\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_rcomp\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers))){\unicdbdjdcd}\\
((r1\_tarski~X0~(k1\_relset\_1~k1\_numbers~(k1\_partfun1~k1\_numbers~\\
k1\_numbers~k1\_numbers~k1\_numbers~k19\_sin\_cos~k2\_fdiff\_9))){\unicdbdjdcd}\\
((r2\_fdiff\_1~(k1\_partfun1~k1\_numbers~k1\_numbers~k1\_numbers~k1\_numbers~\\
k19\_sin\_cos~k2\_fdiff\_9)~X0){\unicdcdcdhd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k1\_numbers){\unicdbdjdcd}\\
((X1 \in X0){\unicdbdjdcd}(k1\_seq\_1~(k2\_fdiff\_1~(k1\_partfun1~k1\_numbers~k1\_numbers~\\
k1\_numbers~k1\_numbers~k19\_sin\_cos~k2\_fdiff\_9)~X0)~X1=k10\_real\_1~\\
(k8\_real\_1~(k1\_seq\_1~k16\_sin\_cos~X1)~(k1\_seq\_1~k19\_sin\_cos~(k1\_seq\_1~\\
k19\_sin\_cos~X1)))~(k5\_square\_1~(k1\_seq\_1~k16\_sin\_cos~(k1\_seq\_1~\\
k19\_sin\_cos~X1))))))))\end{array}
\label{hyp:ehddhdpfggegjgggggpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v2\_measure5~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_funct\_1~\\
X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}\\
(((r1\_tarski~X0~X1){\unicdcdcdhd}((r2\_fdiff\_1~X2~X1){\unicdcdcdhd}((r1\_integra5~X0~(k2\_fdiff\_1~\\
X2~X1)){\unicdcdcdhd}(v1\_comseq\_2~(k2\_partfun1~k1\_numbers~k1\_numbers~(k2\_fdiff\_1~\\
X2~X1)~X0))))){\unicdbdjdcd}(k2\_integra5~X0~(k2\_fdiff\_1~X2~X1)=k9\_real\_1~(k1\_seq\_1~\\
X2~(k4\_seq\_4~X0))~(k1\_seq\_1~X2~(k5\_seq\_4~X0)))))\end{array}
\label{hyp:ehbdddpfjgogehfghgchbgfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v2\_measure5~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}\\
(((r1\_tarski~X0~(k1\_relset\_1~k1\_numbers~X1)){\unicdcdcdhd}(v1\_fcont\_1~(k2\_partfun1~\\
k1\_numbers~k1\_numbers~X1~X0))){\unicdbdjdcd}(r1\_integra5~X0~X1)))\end{array}
\label{hyp:ehbdbdpfjgogehfghgchbgfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v2\_measure5~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}\\
(((r1\_tarski~X0~(k1\_relset\_1~k1\_numbers~X1)){\unicdcdcdhd}(v1\_fcont\_1~(k2\_partfun1~\\
k1\_numbers~k1\_numbers~X1~X0))){\unicdbdjdcd}(v1\_comseq\_2~(k2\_partfun1~k1\_numbers~\\
k1\_numbers~X1~X0))))\end{array}
\label{hyp:ehbdadpfjgogehfghgchbgfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k2\_fdiff\_9){\unicdcdcdhd}(m1\_subset\_1~k2\_fdiff\_9~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))\end{array}
\label{hyp:egehpflgcdpfggegjgggggpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}((v1\_funct\_1~(k2\_fdiff\_1~\\
X0~X1)){\unicdcdcdhd}(m1\_subset\_1~(k2\_fdiff\_1~X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers))))\end{array}
\label{hyp:egehpflgcdpfggegjgggggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1)))){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X2~X3))))){\unicdbdjdcd}((v1\_funct\_1~(k1\_partfun1~X0~X1~X2~X3~X4~X5)){\unicdcdcdhd}(m1\_subset\_1~\\
(k1\_partfun1~X0~X1~X2~X3~X4~X5)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X3))))\end{array}
\label{hyp:egehpflgbdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k19\_sin\_cos){\unicdcdcdhd}((v1\_funct\_2~k19\_sin\_cos~k1\_numbers~\\
k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~k19\_sin\_cos~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers))))\end{array}
\label{hyp:egehpflgbdjdpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (r2\_fdiff\_1~X0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~\\
k1\_numbers)))){\unicdbdjdcd}((X2=k2\_fdiff\_1~X0~X1){\unicdbdjded}((k1\_relset\_1~k1\_numbers~\\
X2=X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k1\_numbers){\unicdbdjdcd}((X3 \in X1){\unicdbdjdcd}(k1\_seq\_1~\\
X2~X3=k1\_fdiff\_1~X0~X3)))))))\end{array}
\label{hyp:eghdpfggegjgggggpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddjdpfjgogehfghgchbded}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v2\_measure5~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v3\_rcomp\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~k1\_numbers))){\unicdbdjdcd}\\
(((r1\_tarski~X0~X2){\unicdcdcdhd}(({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k1\_numbers){\unicdbdjdcd}\\
((X3 \in X2){\unicdbdjdcd}(k1\_seq\_1~X1~X3=k10\_real\_1~(k8\_real\_1~(k1\_seq\_1~k16\_sin\_cos~\\
X3)~(k1\_seq\_1~k19\_sin\_cos~(k1\_seq\_1~k19\_sin\_cos~X3)))~(k5\_square\_1~\\
(k1\_seq\_1~k16\_sin\_cos~(k1\_seq\_1~k19\_sin\_cos~X3)))))){\unicdcdcdhd}((r1\_tarski~\\
X2~(k1\_relset\_1~k1\_numbers~(k1\_partfun1~k1\_numbers~k1\_numbers~\\
k1\_numbers~k1\_numbers~k19\_sin\_cos~k2\_fdiff\_9))){\unicdcdcdhd}((X2=k1\_relset\_1~\\
k1\_numbers~X1){\unicdcdcdhd}(v1\_fcont\_1~(k2\_partfun1~k1\_numbers~k1\_numbers~\\
X1~X0)))))){\unicdbdjdcd}(k2\_integra5~X0~X1=k9\_real\_1~(k1\_seq\_1~(k1\_partfun1~\\
k1\_numbers~k1\_numbers~k1\_numbers~k1\_numbers~k19\_sin\_cos~k2\_fdiff\_9)~\\
(k4\_seq\_4~X0))~(k1\_seq\_1~(k1\_partfun1~k1\_numbers~k1\_numbers~k1\_numbers~\\
k1\_numbers~k19\_sin\_cos~k2\_fdiff\_9)~(k5\_seq\_4~X0))))))\end{array}$$
\end{theorem}
\end{document}
