\documentclass{article}
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\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdbdjded{\Leftrightarrow}
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\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t19\_integra3 (TMUjxfhJSqAc7BwKZupuCh5C4vXLsqoLm59)}
\maketitle
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\_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 $ m1\_integra1 : {{\iota}{\unicdbdjdcd}{{\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 $ k2\_zfmisc\_1 : {{\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 $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_seq\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_rvsum\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_seq\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_integra1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v2\_measure5~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_integra1~X2~X1){\unicdbdjdcd}((X0 \in k4\_finseq\_1~\\
X2){\unicdbdjdcd}(r1\_tarski~(k2\_integra1~X1~X2~X0)~X1))))\end{array}
\label{hyp:ehidpfjgogehfghgchbgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\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 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
((v2\_measure5~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~k1\_numbers)))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~X0~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k1\_numbers))))){\unicdbdjdcd}\\
(((v1\_comseq\_2~(k2\_partfun1~X0~k1\_numbers~X2~X0)){\unicdcdcdhd}(r1\_tarski~\\
X1~X0)){\unicdbdjdcd}((r1\_xxreal\_0~(k5\_seq\_4~(k1\_rvsum\_1~X2))~(k5\_seq\_4~(k1\_rvsum\_1~\\
(k2\_partfun1~X0~k1\_numbers~X2~X1)))){\unicdcdcdhd}((r1\_xxreal\_0~(k5\_seq\_4~\\
(k1\_rvsum\_1~X2))~(k4\_seq\_4~(k1\_rvsum\_1~(k2\_partfun1~X0~k1\_numbers~\\
X2~X1)))){\unicdcdcdhd}((r1\_xxreal\_0~(k4\_seq\_4~(k1\_rvsum\_1~(k2\_partfun1~X0~\\
k1\_numbers~X2~X1)))~(k4\_seq\_4~(k1\_rvsum\_1~X2))){\unicdcdcdhd}(r1\_xxreal\_0~\\
(k5\_seq\_4~(k1\_rvsum\_1~(k2\_partfun1~X0~k1\_numbers~X2~X1)))~(k4\_seq\_4~\\
(k1\_rvsum\_1~X2)))))))))\end{array}
\label{hyp:mgbdfdpfjgogehfghgchbgdd}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_numbers}}}}\label{hyp:ggdgbdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k5\_numbers}}~{({{k1\_zfmisc\_1}~{k1\_numbers}})}}\label{hyp:egehpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v2\_measure5~\\
X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers)))){\unicdcdcdhd}((m1\_integra1~\\
X1~X0){\unicdcdcdhd}(v7\_ordinal1~X2))){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k2\_integra1~X0~X1~X2)){\unicdcdcdhd}\\
((v2\_measure5~(k2\_integra1~X0~X1~X2)){\unicdcdcdhd}(m1\_subset\_1~(k2\_integra1~\\
X0~X1~X2)~(k1\_zfmisc\_1~k1\_numbers))))\end{array}
\label{hyp:egehpflgcdpfjgogehfghgchbgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehbdjdpfjgogehfghgchbgdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v2\_measure5~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_integra1~X2~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~X1~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~k1\_numbers))))){\unicdbdjdcd}(((v1\_comseq\_2~\\
(k2\_partfun1~X1~k1\_numbers~X3~X1)){\unicdcdcdhd}(X0 \in k4\_finseq\_1~X2)){\unicdbdjdcd}(r1\_xxreal\_0~\\
(k5\_seq\_4~(k1\_rvsum\_1~X3))~(k4\_seq\_4~(k1\_rvsum\_1~(k2\_partfun1~\\
X1~k1\_numbers~X3~(k2\_integra1~X1~X2~X0)))))))))\end{array}$$
\end{theorem}
\end{document}
