\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\preoh[1]{\lnot #1}
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\begin{document}
\title{t27\_integra7 (TMG8Fe1kBHA2iF6NapUuXcDh8io2tSYz3YT)}
\maketitle
Let $ r1\_integra7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k24\_sin\_cos : {\iota}$ be given.
Let $ v3\_rcomp\_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\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r2\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_subset\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_limfunc1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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.
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}\\
((k2\_fdiff\_1~k24\_sin\_cos~X0=k2\_partfun1~k1\_numbers~k1\_numbers~\\
k24\_sin\_cos~X0){\unicdcdcdhd}(k9\_xtuple\_0~(k2\_partfun1~k1\_numbers~k1\_numbers~\\
k24\_sin\_cos~X0)=X0))\end{array}
\label{hyp:ehfdpfehbgjhmgpgchpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k2\_fdiff\_1}~{k24\_sin\_cos}}~{k1\_numbers}}={k24\_sin\_cos}}\label{hyp:ehddcdpfjgogehfghgchbgid}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v2\_funct\_1~k24\_sin\_cos){\unicdcdcdhd}((r2\_fdiff\_1~k24\_sin\_cos~k1\_numbers){\unicdcdcdhd}\\
((r2\_fdiff\_1~k24\_sin\_cos~(k2\_subset\_1~k1\_numbers)){\unicdcdcdhd}(({\unicdcdadad} X0 .  \\
(m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(k1\_fdiff\_1~k24\_sin\_cos~X0=k1\_seq\_1~\\
k24\_sin\_cos~X0)){\unicdcdcdhd}(({\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(\\
\preoh r1\_xxreal\_0~(k1\_fdiff\_1~k24\_sin\_cos~X0)~k6\_numbers)){\unicdcdcdhd}((k1\_relset\_1~\\
k1\_numbers~k24\_sin\_cos=k2\_subset\_1~k1\_numbers){\unicdcdcdhd}((k1\_relset\_1~\\
k1\_numbers~k24\_sin\_cos=k2\_subset\_1~k1\_numbers){\unicdcdcdhd}(k2\_relset\_1~\\
k1\_numbers~k24\_sin\_cos=k3\_limfunc1~k6\_numbers)))))))\end{array}
\label{hyp:ehbdgdpfehbgjhmgpgchpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}((r2\_relset\_1~X0~X1~X2~X3){\unicdbdjded}(X2=X3))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~\\
X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}\\
((r1\_integra7~X0~X1~X2){\unicdbdjded}((r2\_fdiff\_1~X1~X0){\unicdcdcdhd}(r2\_relset\_1~k1\_numbers~\\
k1\_numbers~(k2\_fdiff\_1~X1~X0)~(k2\_partfun1~k1\_numbers~k1\_numbers~\\
X2~X0)))))\end{array}
\label{hyp:mgbdddpfjgogehfghgchbghd}
\end{equation}
Assume the following.
\begin{equation}
{{v3\_rcomp\_1}~{({{k2\_subset\_1}~{k1\_numbers}})}}\label{hyp:ggdgcdpfggdgpgogehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k24\_sin\_cos){\unicdcdcdhd}((v2\_funct\_1~k24\_sin\_cos){\unicdcdcdhd}(v1\_funct\_2~\\
k24\_sin\_cos~k1\_numbers~k1\_numbers))\end{array}
\label{hyp:ggdgbdpfehbgjhmgpgchpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{m1\_subset\_1}~{({{k2\_subset\_1}~{X0}})}}~{({{k1\_zfmisc\_1}~{X0}})}}}\label{hyp:egehpflgcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k24\_sin\_cos){\unicdcdcdhd}((v1\_funct\_2~k24\_sin\_cos~k1\_numbers~\\
k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~k24\_sin\_cos~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers))))\end{array}
\label{hyp:egehpflgcdedpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k2\_subset\_1}~{X0}}={X0}}}\label{hyp:egddpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdhdpfjgogehfghgchbghd}
${{{{r1\_integra7}~{k1\_numbers}}~{k24\_sin\_cos}}~{k24\_sin\_cos}}$.
\end{theorem}
\end{document}
